Question

Tell the nearest hundredths of a meter that each given measurement is between. \(1.759 \mathrm{m}\)

Short answer

1.76 meters

Step-by-step solution

- Identify the Hundredths Place

Find the hundredths place in the given measurement. The hundredths place is the second digit to the right of the decimal point in the number. In the given measurement of 1.759 meters, the hundredths place is 5.

- Determine the Nearest Hundredths

Look at the digit in the thousandths place, which is the third digit to the right of the decimal point. In the given measurement of 1.759 meters, the thousandths place is 9. Since this digit (9) is greater than or equal to 5, round the hundredths place up by 1.

- Round the Measurement

After rounding up, change the number in the hundredths place from 5 to 6. All digits to the right of the hundredths place become zeros, which are then dropped. Therefore, 1.759 meters rounds to 1.76 meters.

Key concepts

Place Value

Understanding place value is essential when working with decimals. Each digit in a number has a different value depending on its position. For decimals, the place values are:

• Tenths place - the first digit to the right of the decimal point.
• Hundredths place - the second digit to the right of the decimal point.
• Thousandths place - the third digit to the right of the decimal point.

In the number 1.759, for example, the '1' is in the units place, the '7' is in the tenths place, the '5' is in the hundredths place, and the '9' is in the thousandths place. Understanding these placements helps when rounding numbers.

Hundredths Place

The hundredths place is crucial when rounding decimals because it dictates the precision of the rounded number. In any given decimal, the hundredths place is the second digit to the right of the decimal point. For example, in the number 1.759, the digit '5' is in the hundredths place. Identifying the hundredths place correctly is the first step in the rounding process. Once you know where the hundredths place is, you can use it to find the nearest hundredths value for your number.

Rounding Rules

Rounding rules help determine how to adjust numbers based on nearby digits. Here are the steps you follow when rounding to the nearest hundredths:

• Identify the digit in the hundredths place.
• Look at the next digit to the right, in the thousandths place.
• If the thousandths digit is 5 or greater, round the hundredths digit up by one.
• If the thousandths digit is less than 5, keep the hundredths digit the same.

For example, with 1.759, the hundredths digit is '5' and the thousandths digit is '9'. Since '9' is greater than '5', we round the '5' up to '6', giving us 1.76 when rounded to the nearest hundredths.