Problem 36 - Elementary Algebra

Question

$$ \text { Round } 0.0053 \text { to the nearest thousandth. } $$

Step-by-Step Solution

Answer

0.005

Step 1: Identify the Thousandth Place

Locate the thousandth place in the number 0.0053. The thousandth place is the third digit to the right of the decimal point, which is 5 in this case.

Step 2: Check the Next Digit

Look at the digit immediately to the right of the thousandth place, which is the digit 3.

Step 3: Apply Rounding Rules

Since the digit to the right of the thousandth place (3) is less than 5, the thousandth place digit (5) remains the same.

Step 4: Round the Number

The number after rounding to the nearest thousandth is 0.005.

Key Concepts

decimal places

When dealing with decimal numbers, every digit to the right of the decimal point has a specific name based on its position.
These are known as decimal places. For instance, in the number 0.0053, the '0' right after the decimal point is in the tenths place, the next '0' is in the hundredths place, and the '5' is in the thousandths place.
Decimal places are essential because they help us understand the precision of a number. The more decimal places a number has, the more precise it is.
This precision is particularly important in scientific calculations, financial data, and measurements.

rounding rules

Rounding numbers is a crucial skill to simplify figures while retaining as much accuracy as possible.
Basic rounding rules make it easier to manage large or complex numbers in everyday use. Here’s a quick guide to rounding rules:
If the digit to the right of the place value you're rounding to is less than 5, you leave the rounding digit unchanged and drop all remaining digits.
If the digit to the right of the place value you're rounding to is 5 or more, you increase the rounding digit by one and drop all remaining digits.
These rules help ensure that numbers are rounded consistently and correctly.

thousandth place

The thousandth place is the third digit to the right of the decimal point.
For example, in the number 0.0053, the '5' occupies the thousandth place.
Understanding where the thousandth place is helps with accurate rounding. To round a number to the nearest thousandth, you need to look at the digit in this position and then apply rounding rules based on the digit immediately following it.
If we apply this to our example, since the digit in the thousandth place is '5' and the next digit '3' is less than 5, the number becomes 0.005 when rounded.

place value

Place value refers to the value of each digit in a number based on its position.
In decimal numbers, each place to the right of the decimal point decreases by a factor of ten: the tenths, hundredths, thousandths, and so on.
For example, in 0.0053, the '3' is in the ten-thousandths place, the '5' is in the thousandths place, the second '0' is in the hundredths place, and the first '0' is in the tenths place.
Recognizing place value is fundamental for performing arithmetic operations, comparing numbers, and understanding the significance of digits in a number.