Problem 63 - Prealgebra

Question

Complete the following table. $$\begin{array}{|c|c|c|c|} \hline \text {} & \text {} & \text { Round to the Nearest } & \text {} & \text {} \\ \text {Number} & \text { Whole Number } & \text { Tenth } & \text { Hundredth } & \text { Thousand } \\ \hline 0.1562 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

0; 0.2; 0.16; 0

Step 1: Round to the Nearest Whole Number

To round to the nearest whole number, you look at the tenths place. If the tenths digit is 5 or greater, round up the whole number. Otherwise, keep the whole number as is. In 0.1562, the tenths digit is 1, which is less than 5. Thus, 0.1562 rounds down to 0.

Step 2: Round to the Nearest Tenth

To round to the nearest tenth, you examine the hundredths place. If the hundredths digit is 5 or more, round the tenths digit up. Here, the number is 0.1562, and the hundredths place is 5. Therefore, the number rounds up the tenths place from 1 to 2, resulting in 0.2.

Step 3: Round to the Nearest Hundredth

To find the nearest hundredth, you check the thousandths digit. If it is 5 or more, you round up the hundredths digit. In 0.1562, the thousandths place is 6, which is greater than 5. So, round the hundredths place up from 5 to 6, giving you 0.16.

Step 4: Round to the Nearest Thousand

When the original number is less than 1000, like 0.1562, it typically rounds to zero in thousand-value contexts, unless a larger factor applies. Here, it rounds to 0 since 0.1562 is considerably less than 500.

Key Concepts

nearest whole number

Rounding to the nearest whole number simplifies a decimal by only focusing on its integer part. Here's how you can easily do it:

• Check the tenths digit (the first number after the decimal point).
• If this digit is 5 or higher, increase the whole number by one.
• If it's less than 5, keep the whole number unchanged.

In the case of 0.1562, you look at the tenths digit, which is 1. Since 1 is less than 5, we round down, or rather, leave the whole number as 0. The number effectively simplifies to 0 when rounded to the nearest whole number.

nearest tenth

Rounding a number to the nearest tenth involves considering the hundredths place, which is two places after the decimal point. The process centers around determining whether to adjust the tenths digit.

• Identify the number in the hundredths position (second digit after the decimal).
• If it is 5 or more, round up the tenths digit.
• If the hundredths digit is less than 5, the tenths digit remains the same.

For 0.1562, you examine the hundredths digit, 5, which leads you to increase the tenths digit from 1 to 2. Thus, rounding gives you 0.2.

nearest hundredth

To round to the nearest hundredth, you turn your attention to the thousandths place, which is the third digit following the decimal point. This digit decides whether you round the hundredths figure up or down.

• Look at the thousandths digit (the third digit).
• If this digit is 5 or more, increment the hundredths digit by one.
• Maintain the hundredths digit if the thousandths is less than 5.

For the number 0.1562, the thousandths digit is 6, which is higher than 5, so you increase the hundredths digit from 5 to 6. Therefore, the rounded number is 0.16.

place value rounding

Place value rounding involves using each digit's position value to round numbers appropriately. Understanding place values is crucial for accurate rounding, whether to a whole number, tenth, hundredth, or beyond.

• Whole numbers are rounded using the tenths digit.
• For tenths rounding, the hundredths place guides the adjustment.
• In rounding to the nearest hundredth, the thousandths place dictates the change.
• The rounding for thousand or larger values often revolves around the number's general size (e.g., less than 500 rounds down to 0 in the thousands).

With 0.1562, its place values guided distinct decisions at each step to arrive at numbers such as 0, 0.2, and 0.16, respectively.