Question

1. write the decomposition that helps you, and then round to the given place value. draw number lines to explain your thinking. circle the rounded value on each number line. a. 43.586 to the nearest tenth, hundredth, and one.

Explanation:

Step1: Decompose 43.586

The number \( 43.586 \) can be decomposed as \( 40 + 3 + 0.5 + 0.08 + 0.006 \).

Step2: Round to the nearest tenth

The tenths place is the first digit after the decimal, which is \( 5 \). The next digit (hundredths place) is \( 8 \), which is greater than or equal to \( 5 \). So we round up the tenths place.
\( 43.586 \approx 43.6 \) (to the nearest tenth)

Step3: Round to the nearest hundredth

The hundredths place is the second digit after the decimal, which is \( 8 \). The next digit (thousandths place) is \( 6 \), which is greater than or equal to \( 5 \). So we round up the hundredths place.
\( 43.586 \approx 43.59 \) (to the nearest hundredth)

Step4: Round to the nearest one (whole number)

The ones place is \( 3 \). The next digit (tenths place) is \( 5 \), which is greater than or equal to \( 5 \). So we round up the ones place.
\( 43.586 \approx 44 \) (to the nearest one)

Answer:

• Nearest tenth: \( 43.6 \)
• Nearest hundredth: \( 43.59 \)
• Nearest one: \( 44 \)

(Note: For drawing number lines:

• For nearest tenth: Draw a number line between \( 43.5 \) and \( 43.6 \). Mark \( 43.586 \) closer to \( 43.6 \), then circle \( 43.6 \).
• For nearest hundredth: Draw a number line between \( 43.58 \) and \( 43.59 \). Mark \( 43.586 \) closer to \( 43.59 \), then circle \( 43.59 \).
• For nearest one: Draw a number line between \( 43 \) and \( 44 \). Mark \( 43.586 \) closer to \( 44 \), then circle \( 44 \).)