Question

Arrange the following decimals from smallest to largest: 0.64,4.6,0.46 ______

Short answer

0.46, 0.64, 4.6

Step-by-step solution

Understand the Problem

We need to arrange the given decimal numbers in ascending order, which means from the smallest to the largest. The decimals given are 0.64, 4.6, and 0.46.

Compare Decimals

Let's compare the decimal numbers by their value. Identify the value before the decimal point first as it's more significant. For 0.64 and 0.46, they both start with '0,' but 4.6 starts with '4.' Hence, 4.6 is greater than both 0.64 and 0.46.

Compare 0.64 and 0.46

Since 0.64 and 0.46 both have '0' before the decimal, we need to compare their decimal parts. Compare '64' and '46' after the decimal. "64" is greater than "46," so 0.64 is greater than 0.46.

Arrange the Numbers

Now, arrange the numbers based on the comparison: 0.46 < 0.64 < 4.6. Thus, 0.46 is the smallest, followed by 0.64, and 4.6 is the largest.

Key concepts

Arranging Numbers

Arranging numbers, especially when dealing with decimal numbers, is about placing them in order, either from smallest to largest (ascending order) or vice versa. In the context of our given problem, we need to arrange the numbers in ascending order. This means you need to identify which number is the smallest, which comes next, and which is the largest.

Start by checking the whole numbers before the decimal point. If these numbers are different, it's straightforward; the smaller number precedes the larger one. If they are the same, like in our example with decimals, you'll compare parts that come after the decimal.

Don't rush through each number. Take your time to understand each part of the number. This will help you compare them accurately and arrange them correctly. Practice makes perfect, so keep arranging numbers to get comfortable with the process.

Decimal Numbers

Decimal numbers consist of whole numbers and fractions written together in a single number with a decimal point separating them. Understanding decimals is key to comparing them.

For example, in the number '0.64', '0' is the whole number part, while '64' is the fractional part. The decimal point shows us how to read these digits correctly.

When you have decimal numbers to compare, look at the whole number first. If they're equal, like in our decimals '0.64' and '0.46', then you need to move to the digits after the decimal point and compare those. Remember, a higher number in the decimal part means a larger value.

Decimals allow us to express values between whole numbers, making comparisons possible when dealing with fractions. They are essential in everyday math, especially with money, measurements, and scientific values.

Place Value

Place value is a fundamental concept in mathematics that helps us understand the value of digits in any given number, including decimals. It tells us how much each digit in a number is worth depending on its position.

For decimal numbers, the digits to the left of the decimal point are whole numbers and increase tenfold as you move leftward. The digits to the right of the decimal point represent fractions, with each place value dividing by ten as you move rightward.

For instance, in '4.6', the '4' is in the units place, meaning it counts as four whole units, while the '6' is in the tenths place, meaning six-tenths.

Understanding place value ensures that you can accurately compare numbers by evaluating each digit's contribution to the overall number. Practicing this concept will help you become more skilled in mathematical operations involving decimals.