1-2. Significant Figures And Scientific Notation

1.

How many significant figures are in the following value: 351.0 cm

Explanation
ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. Thus, the digits 3, 5, 1, and 0 are all significant.

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4
2.

Bob measured the width of a cardboard box to be 640 cm. As written, which of the following digits in his measurement is/are significant? Check all that apply.
- A.
  
  6
- B.
  
  4
- C.
  
  0
Correct Answer(s)
A. 6
B. 4

Explanation
ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. The zero in this case is not significant.

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3.

Sally found that the mass of an unknown solid is 0.5200 g. True or False: The rightmost zero in 0.5200 g is a significant digit.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
It takes a lot of practice get familiar with significant figure rules and determine whether a zero is significant. ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant. Also, ALL zeroes between non-zero numbers are ALWAYS significant; Thus, thel zero written in the third decimal place is also significant. The leftmost zero (to the left of the decimal point) is not significant.

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4.

2.55 mL + 45.723 mL + 0.30 mL = _____. (The correct answer will have the correct number of significant figures.)
- A.
  
  48.573 mL
- B.
  
  48.57 mL
- C.
  
  48.6 mL
- D.
  
  49 mL
Correct Answer
B. 48.57 mL

Explanation
When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement. Thus, look at each number you are adding/subtracting and see how digits are to the right of the decimal place. The answer will have the same number of digits to the right of the decimal place as the smallest number of decimal places of the number you are adding. In this case, we are adding 2.55 (2 to the right), 45.723 (3 to the right), and 0.30 (2 to the right). The smallest number of places to the right is 2 digits; thus, the answer must be rounded to 2 decimal places.

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1
0
5.

4.56 km * 35.6 km = _____ km. (Note: the correct answer will have the correct number of significant figures.)

Correct Answer
162 km
162
162km

Explanation
When multiplying/dividing numbers, the answer will have the same number of significant figures as the smallest number of significant figures you multiplied/divided. In this case, we are multiplying 4.56 (3 significant figures) and 35.6 (3 significant figures). Thus, the answer will also have 3 significant figures.

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6.

How many significant figures are in the answer for the following calculation?:
- A.
  
  2
- B.
  
  3
- C.
  
  4
- D.
  
  5
Correct Answer
A. 2

Explanation
Following the order of operations, add the two numbers in the numerator first. When you add/subtract, round the answer to the small number of decimal places. In this case, we are adding 3.4 (1 to the right) and 5.678 (3 to the right); thus, the answer will have 1 digit to the right of the decimal place. The answer to that addition section is 9.1. Now, we need to divide: 9.1/235. When you multiply/divide, the answer will have the same number of significant figures as the number with the lowest number of significant figures. In this case, we are dividing 9.1 (2 significant figures) and 235 (3 significant figures); thus, the answer will have 2 significant figures. The correct answer to this calculation, with the correct number of significant figures, is 0.039 (2 significant figures).

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7.

Vance wants to write the number 5670000 in scientific notation. Fill in the blank:

Correct Answer
5.67

Explanation
The given answer, 5.67, is the correct way to write the number 5670000 in scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. The coefficient should be a number between 1 and 10, and in this case, it is 5.67. The power of 10 is determined by the number of zeros in the original number, which is 6 in this case. Therefore, the number 5670000 can be written as 5.67 x 10^6 in scientific notation.

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8.

Express the number 0.000466 in scientific notation by filling in the exponent:

Correct Answer
-4

Explanation
To express a number in scientific notation, we move the decimal point to a position where there is only one non-zero digit to the left of it. In this case, the original number is 0.000466. By moving the decimal point 4 places to the right, we get 4.66. Since we moved the decimal point to the right, the exponent is negative. Therefore, the number 0.000466 in scientific notation with an exponent of -4 is 4.66 x 10^-4.

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9.

Express the following number in expanded form:
- A.
  
  78,600
- B.
  
  7,860
- C.
  
  768
- D.
  
  76.8
Correct Answer
B. 7,860

Explanation
The given number is 7,860. In expanded form, this number can be expressed as 7,000 + 800 + 60.

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0
3
10.

Express the following number in expanded form:
- A.
  
  0.000002563
- B.
  
  0.00002563
- C.
  
  2,563
- D.
  
  256,300
Correct Answer
B. 0.00002563

Explanation
The given answer, 0.00002563, is the expanded form of the number. It represents 2 hundredths, 5 thousandths, 6 ten-thousandths, and 3 hundred-thousandths.

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1-2. Significant Figures And Scientific Notation

How many significant figures are in the following value: 351.0 cm

Bob measured the width of a cardboard box to be 640 cm. As written, which of the following digits in his measurement is/are significant? Check all that apply.

Sally found that the mass of an unknown solid is 0.5200 g. True or False: The rightmost zero in 0.5200 g is a significant digit.

2.55 mL + 45.723 mL + 0.30 mL = _____. (The correct answer will have the correct number of significant figures.)

4.56 km * 35.6 km = _____ km. (Note: the correct answer will have the correct number of significant figures.)

How many significant figures are in the answer for the following calculation?:

Vance wants to write the number 5670000 in scientific notation. Fill in the blank:

Express the number 0.000466 in scientific notation by filling in the exponent:

Express the following number in expanded form:

Express the following number in expanded form: