Question

Approximate each number (a) rounded and (b) truncated to three decimal places. $$ \frac{521}{15} $$

Short answer

Rounded: 34.733; Truncated: 34.733

Step-by-step solution

Calculate the Division

First, calculate the division of the numbers provided. In this case, divide 521 by 15. The result is approximately 34.733333.

Round to Three Decimal Places

To round the result to three decimal places, look at the fourth decimal. Since it is '3' which is less than 5, round down. The rounded result to three decimal places is 34.733.

Truncate to Three Decimal Places

To truncate the result to three decimal places, simply cut off any digits beyond the third decimal place, regardless of their value. The truncated result to three decimal places is 34.733.

Key concepts

rounding

Rounding numbers is a useful technique for approximating values. It involves adjusting a number to make it simpler while maintaining a close value to the original.
When rounding to three decimal places, you look at the fourth decimal place to decide whether to round up or down.
If the fourth decimal place is 5 or higher, you round up the third decimal place by one. Otherwise, you round down and keep the third decimal place as it is.
For example, with the number 34.733333, we inspect the fourth decimal place (which is a 3). Since 3 is less than 5, we round down, resulting in 34.733.

truncating

Truncating numbers means cutting off digits beyond a certain point without rounding. It's a straightforward method to approximate numbers.

When you're truncating to three decimal places, you simply remove any digits beyond the third decimal place.
This method does not consider the value of the digits being removed.
For the example 34.733333, truncating to three decimal places would discard everything after the third decimal place, giving us 34.733.
This process can be helpful when you need a quick and precise cutoff without any rounding.

decimal places

Decimal places refer to the number of digits after the decimal point in a number. They are crucial in understanding the precision of a number.
Different tasks may require different levels of precision.

When you round or truncate to three decimal places, you are specifying that the number should be precise to the thousandths place.

1. The first decimal place is the tenths.
2. The second decimal place is the hundredths.
3. The third decimal place is the thousandths.

For example, in the number 34.733, '7' is in the tenths place, '3' is in the hundredths place, and the second '3' is in the thousandths place.

division

Division is a fundamental mathematical operation used to find out how many times one number is contained within another. It consists of a dividend (the number to be divided) and a divisor (the number by which we divide).

In our exercise, 521 is the dividend, and 15 is the divisor. The division operation gives us the quotient, which in this case is approximately 34.733333.

Performing accurate division is crucial for subsequent steps like rounding and truncating, as the initial result directly impacts the final approximated values.