Question

1. convert the following using your metric number line:

a. convert 4.5g into kg
b. convert 70 m into cm

Explanation:

Step1: Recall metric prefixes

We know that \(1\space kg = 1000\space g=10^{3}\space g\), so to convert grams to kilograms, we divide by \(10^{3}\) (or move the decimal point 3 places to the left). For part a, we have \(4.5\space g\) to \(kg\).
\(4.5\space g=\frac{4.5}{10^{3}}\space kg = 4.5\times 10^{- 3}\space kg = 0.0045\space kg\)

Step2: Recall metric prefixes for length

We know that \(1\space m=100\space cm = 10^{2}\space cm\), so to convert meters to centimeters, we multiply by \(10^{2}\) (or move the decimal point 2 places to the right). For part b, we have \(70\space m\) to \(cm\).
\(70\space m=70\times10^{2}\space cm=70\times100\space cm = 7000\space cm\)

Answer:

a. \(0.0045\space kg\)
b. \(7000\space cm\)