The mass of a paperclip is 9.0 × 10−4 mg. If a box of paperclips has 6.14 × 104 paperclips, determine the total mass of the paperclips in the box. Write the final answer in scientific notation with the correct number of significant digits.
a) 2.86 × 100 mg
b) 5 × 101 mg
c) 5.5 × 101 mg
d) 5.526 × 101 mg
To find the total mass of the paperclips in the box, we need to multiply the mass of one paperclip by the number of paperclips in the box.
Mass of one paperclip = 9.0 × 10^(-4) mg
Number of paperclips in the box = 6.14 × 10^4
Total mass of paperclips = (9.0 × 10^(-4) mg) * (6.14 × 10^4) = 5.526 × 10^(0) mg
Since the answer should be in scientific notation with the correct number of significant digits, we can round the answer to two significant digits.
Therefore, the final answer is d) 5.526 × 10^1 mg.
To determine the total mass of the paperclips in the box, we need to multiply the mass of a single paperclip by the total number of paperclips.
Given:
Mass of a paperclip = 9.0 × 10^(-4) mg
Number of paperclips in the box = 6.14 × 10^4 paperclips
To find the total mass of the paperclips, we will multiply these values together:
Total mass = (9.0 × 10^(-4) mg) * (6.14 × 10^4 paperclips)
Calculating this multiplication:
Total mass = (9.0 * 6.14) × (10^(-4) * 10^4) mg
Total mass = 55.26 × 10^0 mg
To put this value in scientific notation, we need to move the decimal point to the appropriate position. In this case, we move it one place to the left:
Total mass = 5.526 × 10^1 mg
The correct answer is (d) 5.526 × 10^1 mg.
To determine the total mass of the paperclips in the box, we need to multiply the mass of a single paperclip by the number of paperclips in the box.
Step 1: Convert the mass of a single paperclip to grams.
The mass of a single paperclip is given in milligrams (mg). To convert milligrams to grams, we divide by 1000 since there are 1000 milligrams in a gram.
9.0 × 10^(-4) mg = 9.0 × 10^(-4) / 1000 g
Step 2: Multiply the mass of a single paperclip by the number of paperclips in the box.
(9.0 × 10^(-4) / 1000 g) × (6.14 × 10^4 paperclips)
To multiply the values in scientific notation, multiply their coefficients and add their exponents.
(9.0 × 10^(-4) / 1000) × (6.14 × 10^4)
= (9.0 × 6.14) × (10^(-4) × 10^4)
= 55.26 × 10^(0)
= 5.526 × 10^1 g
Step 3: Convert the mass from grams to milligrams.
To convert grams to milligrams, multiply by 1000 since there are 1000 milligrams in a gram.
5.526 × 10^1 g = 5.526 × 10^1 × 1000 mg
= 5.526 × 10^4 mg
Therefore, the total mass of the paperclips in the box is 5.526 × 10^4 mg.
Comparing the answer to the given choices, we can see that the correct answer is (d) 5.526 × 10^1 mg.