Question

Use prefix multipliers to express each measurement without exponents.

1) 35.6 ×10⁵ g
2) 17.7 ×10⁻¹ g
3) 36.7 ×10 ¹ ¹ g
4) 87.8 ×10−3· g

Answer 1

To express the given measurements without exponents, they can be converted to 3.56 Mg for 35.6 × 10⁵ g, 1.77 g for 17.7 × 10⁻¹ g, 36.7 kg for 36.7 × 10¹¹ g, and 87.8 mg for 87.8 × 10⁻³ g. Metric prefixes help to maintain numerical values between one and a thousand for ease of use.

Step-by-step explanation:

To express each measurement using prefix multipliers without exponents and in grams, we'll convert these into more intuitive numbers by applying the appropriate SI prefixes. Here's how you can express them:

• 35.6 × 10⁵ g becomes 3.56 × 10³ kg or 3.56 Megagrams (Mg), as 1 Mg = 10³ kg.
• 17.7 × 10⁻¹ g becomes 1.77 g, since moving the decimal place one position to the left is equivalent to multiplying by 10⁻¹.
• 36.7 × 10¹¹ g becomes 3.67 × 10· kg or 36.7 Kilograms (kg), as 1 kg = 10³ g.
• 87.8 × 10⁻³ g becomes 0.0878 g or 87.8 Milligrams (mg), as 1 mg = 10⁻³ g.

When using metric prefixes, it's important to choose a unit scale that results in a numerical value greater than one but less than a thousand for ease of reading and practical usage, as seen with the example of using 'kg' instead of 'g' or 'dag' for a 6.5 kg mass.