Measurements, Significant Figures and Scientific Notation

The measurement 0.00023 g has two significant figures because the non-zero digits (2 and 3) are significant, and the zeros before the non-zero digits are not significant.

The metric system is a decimal-based system of measurement used worldwide. It is based on units of ten, making it easy to convert between different units. In the metric system, the base unit for length is the meter. The meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second. It is a fundamental unit of length and is used as a reference for measuring longer or shorter distances.

The measurement 0.00130 cm has three significant figures. This is because all the digits in the number, 1, 3, and 0, are non-zero digits and are therefore significant. The zeros that come after the non-zero digits are also significant as they indicate the precision of the measurement.

The number 4.153 has four significant figures. A significant figure is any digit that contributes to the precision of a number. In this case, all the digits (4, 1, 5, and 3) are significant as they provide information about the precision of the measurement. Therefore, the number 4.153 has four significant figures.

The number 100 has only one significant figure because there is only one non-zero digit in the number. The zero at the end does not count as a significant figure because it is a trailing zero and not necessary for the accuracy or precision of the number.

The given expression is in scientific notation, where a number is written as a product of a decimal number and a power of 10. In this case, 8.55 is multiplied by 10 raised to the power of 1. To convert it into a regular number, we simply move the decimal point one place to the right, resulting in 85.5.

The measurement 0.00560 mg has three significant figures. The leading zeros in the number are not significant, so they do not count. The significant figures are 5, 6, and 0. The zeros between the significant figures are also significant. Therefore, the measurement has three significant figures.

To convert milliliters (mL) to liters (L), you divide the value in milliliters by 1000. In this case, 350 mL divided by 1000 equals 0.350 L.

The largest mass among the given options is 5 kg. This is because kg stands for kilogram, which is a larger unit of mass compared to g (grams), cg (centigrams), and mg (milligrams). Therefore, 5 kg is the correct answer as it represents the greatest mass.

The given expression, -9.37 x 10^-3, is in scientific notation. To convert it into a regular number, we need to move the decimal point three places to the left because the exponent is negative. This gives us -0.00937. Therefore, both -0.00937 and - 0.00937 are correct representations of the regular number equivalent of -9.37 x 10^-3.

The given answer, 3.98 x 10^8, is in scientific notation. Scientific notation is used to represent very large or very small numbers in a compact form. In this case, 3.98 x 10^8 means that the number is 3.98 multiplied by 10 raised to the power of 8. This means that the decimal point is moved 8 places to the right, resulting in a very large number.

The given expression is a subtraction problem where 56.3812 is being subtracted by 15. According to significant figure rules, when performing subtraction, the result should be rounded to the same number of decimal places as the number with the fewest decimal places. In this case, 15 has no decimal places, so the answer should also have no decimal places. Therefore, the correct answer is 41, 41.

The shortest length is 10 mm because millimeters (mm) are smaller units of measurement compared to centimeters (cm), meters (m), and kilometers (km). Therefore, 10 mm is shorter than 1000 cm, 0.100 m, and 0.010 km.

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The measurement 86.000 mL has five significant figures. Significant figures are the digits in a number that carry meaning in terms of precision. In this case, all the digits, including the zeros after the decimal point, are considered significant because they provide information about the precision of the measurement. Therefore, the measurement has five significant figures.

When expressing a number in scientific notation, the coefficient should be a number between 1 and 10, and the exponent should indicate the number of decimal places the decimal point needs to be moved to the right to obtain the original number. In this case, the original number is 3760.289, and the coefficient 3.76 is the closest number between 1 and 10. Moving the decimal point three places to the right gives us the original number, so the correct way to display the answer with three significant figures is 3.76 x 10^3.

The given number, 2.40 x 10^3, has three significant figures. Significant figures are the digits in a number that carry meaning or contribute to its precision. In this case, the digits 2, 4, and 0 are all significant because they are non-zero and are between the decimal point and the first non-zero digit. The exponent 3 does not affect the number of significant figures. Therefore, the number has three significant figures.

When adding numbers in scientific notation, the exponents must be the same. In this problem, both numbers have a power of 10 raised to the -3. Therefore, we can add the coefficients: 3.6 + 4.8 = 8.4. The result is 8.4 x 10^-3. However, we need to express the answer with the proper significant figures, which is 2 in this case. Therefore, the final answer is 5.1 x 10^-3.

When performing addition, the rule is to round the final answer to the least number of decimal places present in any of the numbers being added. In this case, the number with the least number of decimal places is 12.1 g, which has one decimal place. Therefore, the final answer must also have only one decimal place.

The given measurement, 101000 grams, can be converted to scientific notation by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we move the decimal point four places to the left, resulting in 1.01. The exponent of 10 is determined by the number of places the decimal point was moved, which is 5 in this case. Therefore, the correct answer is 1.01 x 10^5 g.

The correct answer is 75 cm^3 because 1 mL is equal to 1 cm^3. Therefore, to convert 75 mL into cm^3, we simply keep the same value and unit.

The given expression involves multiplying two numbers, 9.00 and 0.200, while observing the significant figure rules. The rule states that the answer should have the same number of significant figures as the least precise number in the calculation. In this case, 0.200 has three significant figures, so the answer should also have three significant figures. Therefore, the correct answer is 1.80.

The correct scientific notation for 705000 is 7.05 x 10^5. This is because in scientific notation, the number is expressed as a decimal between 1 and 10, multiplied by a power of 10. In this case, 7.05 is the decimal between 1 and 10, and 10^5 represents the power of 10 that needs to be multiplied.

The given expression is (4.9 x 10^-6) / (7 x 10^-3). To divide numbers in scientific notation, we divide the coefficients and subtract the exponents. So, (4.9 / 7) x 10^(-6 - (-3)) simplifies to 0.7 x 10^-9. However, to properly represent the answer in scientific notation, we need to move the decimal point one place to the right, resulting in 7.0 x 10^-10. Therefore, the correct answer is 7 x 10^-10.

There are 1 million millimeters in 1 kilometer. This is because there are 1000 meters in a kilometer, and 1000 millimeters in a meter. Therefore, to convert kilometers to millimeters, we multiply by 1000 twice, resulting in 1 million millimeters.

The given expression involves the addition of three numbers. When adding numbers with different decimal places, it is important to consider significant figures. In this case, the number 0.01 has two significant figures, 5.632 has four significant figures, and 3.8 has two significant figures. According to the significant figure rules for addition, the result should be rounded to the least number of decimal places in any of the numbers being added, which is one decimal place in this case. Thus, the sum of 0.01, 5.632, and 3.8 is 9.4.

The given number, 0.90985, has five decimal places. To round it to three significant figures, we start from the leftmost non-zero digit and count three digits, including that digit. The fourth digit, 8, is greater than or equal to 5, so we round up the third digit, which is 9. Therefore, the rounded value is 0.910.

When dividing, the result should have the same number of significant figures as the least precise value involved in the calculation. In this case, the least precise value is 150, which has three significant figures. Therefore, the result should also have three significant figures. The correct answer, 0.70, has three significant figures and follows the significant figure rules.

The number 10 x 10^3 can be written as 10,000. In this number, there is only one non-zero digit, which is 1. Therefore, there is only one significant figure in this number.

One meter is equal to 1 x 10^6 micrometers. This is because the prefix "micro" represents one millionth of a unit. Therefore, when converting from meters to micrometers, we multiply by 1 x 10^6.

The volume of water shown in the graduated cylinder is 36.6 mL.

The given number, 0.006580, can be expressed in scientific notation as 6.580 x 10^-3. In scientific notation, the number is written as a decimal between 1 and 10, multiplied by a power of 10. In this case, the decimal is 6.580, and it is multiplied by 10 raised to the power of -3, which means the decimal point is moved 3 places to the left.

The longest distance among the given options is 500 m. This is because 500 m is longer than 3000 mm, 5000 cm, and 0.400 km.

When dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, both 9.000 and 3.0 have four significant figures. Therefore, the result should also have four significant figures. However, since the division result is a whole number (3), it is necessary to include a decimal point and trailing zeros to maintain the four significant figures. Therefore, the correct answer is 3.0.

The correct answer is 265.72 g because it is the only option that includes a decimal point, indicating a more precise measurement. The other options are rounded numbers, which would not be recorded on a balance that can measure to the hundredth place.

The number 1050 has four significant figures because all the digits in the number are non-zero and are therefore significant.

When multiplying numbers with significant figures, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, 0.05 has two significant figures, while 25 has two significant figures as well. Multiplying them together gives us 1.25, which has two significant figures. Therefore, the correct answer is 1.25.

The product of 117 and 42.3 is 4949.1. According to the significant figure rules, the answer should have the same number of significant figures as the measurement with the least number of significant figures, which is 42.3 in this case. Therefore, the answer should be rounded to three significant figures, resulting in 4.95 x 10^3.

The length of the line in the image is 12.5 cm.

The length of the red line in the image is 2.34 cm.

The given expression involves division, and according to significant figure rules, the result should have the same number of significant figures as the number with the least number of significant figures in the expression. In this case, the number 0.006 has only one significant figure. Therefore, the result should also have one significant figure. The answer "1 x 10^6" has one significant figure and is correct.

The given expression involves division and subtraction. According to the significant figure rules, the final answer should have the same number of decimal places as the measurement with the least number of decimal places. In this case, both 24.4 and 15.3 have one decimal place. Therefore, the answer should also have one decimal place. The correct answer, 4.5, satisfies this condition and is the best approximation of the result.

The red line is being measured with a metric ruler, which means that the units of measurement are in centimeters. The first decimal place that is uncertain refers to the accuracy of the measurement. Since the ruler has markings up to the tenths of a centimeter, it means that the measurement can only be estimated to the nearest tenth of a centimeter. Therefore, the correct answer is tenths of a centimeter.

The two equivalent lengths in the given options are 0.070 km and 7000 cm. This is because 0.070 km is equal to 70 meters (since 1 km = 1000 m), and 7000 cm is also equal to 70 meters (since 1 meter = 100 cm). Therefore, both 0.070 km and 7000 cm represent the same length of 70 meters.

The first conversion, 100 mm = 1 cm, is incorrect because 100 mm is equal to 10 cm, not 1 cm. The second conversion, 500 cm = 0.5 m, is also incorrect because 500 cm is equal to 5 m, not 0.5 m.

The given expression involves subtraction and division. When subtracting, we consider the number with the least number of decimal places, which is 13. When dividing, we consider the number with the least number of significant figures, which is 3.90. Therefore, the result should have the same number of decimal places as the number being subtracted (13) and the same number of significant figures as the number being divided (3.90). Hence, the correct answer is -1.

The length of the line in the image is 12.50 because it is the only option that includes two decimal places. The other options either have no decimal places or only one decimal place, which makes them incorrect.

The average mass of the glass can be found by adding up the four measured masses and then dividing by the number of measurements. Adding up the masses gives a total of 399.021 g. Dividing this by 4 gives an average of 99.75525 g. Since the question asks for the answer in the proper number of significant figures, we round the average to three significant figures, which gives us 100.0 g. Therefore, the correct answer is 100.0 g.

The volume in the graduated cylinder is 6.30. This is because the number is written with two decimal places, indicating a high level of precision. The additional zero after the decimal point suggests that the measurement was taken to the nearest hundredth.