Significant Figures And Scientific Notation Practice Quiz

Explanation
The number 305500 has four significant figures. Significant figures are the digits that carry meaning in a number and indicate its precision. In this case, all the non-zero digits (3, 0, 5, and 5) are significant, and the trailing zeros are also not significant. Therefore, the number has a total of four significant figures.

Explanation
The given number, 4.57 x 10^7, is written in scientific notation. In scientific notation, the coefficient is written as a number between 1 and 10, and the exponent indicates the power of 10. The significant figures are the digits that carry meaning in a number. In this case, the coefficient 4.57 has three significant figures: 4, 5, and 7. The exponent does not affect the number of significant figures. Therefore, the correct answer is 3.

Explanation
The given number, 0.00056006, has 5 significant figures. Significant figures are the digits in a number that carry meaning in terms of its precision. In this case, all the digits from the first non-zero digit (5) to the last non-zero digit (6) are significant. The zeros at the beginning and end of the number are not significant as they are only placeholders. Therefore, the number has a total of 5 significant figures.

Explanation
The given number, 930000000000, has two significant figures. Significant figures are the digits in a number that carry meaning and contribute to its precision. In this case, the zeros at the end of the number are not considered significant because they only indicate the magnitude or scale of the number. Therefore, the significant figures in this number are 9 and 3.

Explanation
The number 5.48008 has six significant figures. Significant figures are the digits in a number that carry meaning in terms of its precision. In this case, all the digits, including the trailing zeros after the decimal point, are considered significant because they provide information about the accuracy of the measurement. Therefore, the number has a total of six significant figures.

Explanation
The number 1.00 has three significant figures. The zeros at the beginning and end of the number are considered significant because they are between nonzero digits. The decimal point does not affect the significant figures.

Explanation
The number 100 has only one significant figure because trailing zeros are not considered significant unless there is a decimal point explicitly shown. In this case, there is no decimal point, so only the non-zero digit (1) is considered significant.

Explanation
When you multiply numbers, the result should have the same number of significant figures as the number with the fewest significant figures among the factors.
In this case, both 42 and 5 have only two significant figures each. Therefore, the result should also have two significant figures.
42 x 5 = 210
So, the answer is 210 with two significant figures.

Explanation
When adding or subtracting numbers, the result should be rounded to the same number of decimal places as the number with the fewest decimal places. In this case, both numbers have one decimal place. When we add 54.4 and 45.5, the result is 99.94. Since 99.94 has two decimal places, we round it to one decimal place, which gives us 99.9. Therefore, the correct answer is 99.9.

Explanation
To calculate the answer to the correct number of significant figures, follow these steps:
Perform the division: 405 / 50 = 8.1
Determine the number of significant figures in each of the original numbers:
405 has 3 significant figures.
50 has 1 significant figure.
When dividing or multiplying, the result should have the same number of significant figures as the original number with the fewest significant figures. In this case, 50 has the fewest significant figures (1).
Therefore, the answer should be rounded to 1 significant figure.
So, the result is 8 (rounded to 1 significant figure).

Explanation
The answer, calculated to the correct number of significant figures, is 21.4 x 10^12.When multiplying two numbers in scientific notation, we multiply the coefficients (the numbers in front of 10) and add the exponents of 10. In this case:(4.00 x 10^7) x (5.34 x 10^5) = 4.00 x 5.34 x 10^(7+5) = 21.36 x 10^12However, we need to consider significant figures. Looking at the given numbers, both have three significant figures. When multiplying numbers with the same precision, the resulting number's precision is also three significant figures.So, rounding to three significant figures, we get 21.4 x 10^12, which is the final answer with the correct number of significant figures.

Explanation
To calculate the answer to the correct number of significant figures, follow these steps:
Step 1: Perform the calculation without considering significant figures.
(7.4 x 10^-3) / (6.77 x 10^4) = (7.4 / 6.77) x 10^(-3 - 4) = 1.09393346431 x 10^-7
Step 2: Round the result to the correct number of significant figures. In this case, you should round it to 3 significant figures because the least number of significant figures in the original values is 3 (7.4 and 6.77).
So, rounding to 3 significant figures, the result is:
1.09 x 10^-7
Therefore, the answer to the correct number of significant figures is 1.09 x 10^-7.

Explanation
The given number, 6700000, can be converted into 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, the decimal point is moved 6 places to the left, resulting in the number 6.7. The exponent is determined by the number of places the decimal point was moved, which is 6. Therefore, the correct scientific notation for 6700000 is 6.7 x 10^6.

Explanation
The given number, 0.0000000567, can be expressed in scientific notation as 5.67 x 10^-8. In scientific notation, a number is written as a decimal between 1 and 10 multiplied by a power of 10. In this case, the decimal part is 5.67, and the power of 10 is -8, indicating that the decimal point needs to be moved 8 places to the left to obtain the original number. Therefore, 5.67 x 10^-8 is the correct scientific notation for 0.0000000567.

Explanation
The given number in scientific notation, 4.75 x 10^-4, can be converted to a normal number by moving the decimal point four places to the left. This gives us 0.000475. Therefore, the correct answer is 0.000475.

Explanation
The given number is in scientific notation, where 5.678 is multiplied by 10 raised to the power of 7. To convert it to a normal number, we need to move the decimal point 7 places to the right, resulting in 56,780,000. Therefore, the correct answer is 56,780,000.