Question

Multiply the following numbers by moving the decimal. $0.08\times 10=$ ______

Short answer

0.08 times 10 equals 0.8 by moving the decimal point right.

Step-by-step solution

Understand the Problem

We need to multiply the number 0.08 by 10. The multiplication involves a process called 'moving the decimal point' due to the powers of 10.

Identify the Initial Decimal Position

The original number is 0.08, which has the decimal point between 0 and 0. The number is currently written as 0.08 (two decimal places).

Move the Decimal Point

Multiplying by 10 shifts the decimal point one place to the right. Therefore, move the decimal point from between 0 and 0 in 0.08, one place to the right.

Result of the Multiplication

After moving the decimal point one place to the right, the number 0.08 becomes 0.8. Therefore, 0.08 multiplied by 10 equals 0.8.

Key concepts

Decimal Point Movement

Decimal point movement is a fundamental concept when you've got numbers with decimals and you need to multiply or divide by powers of ten. Imagine that decimal point as a busy traveler moving along the numerical highway. When you multiply a number like 0.08 by 10, the decimal point moves one place to the right.
Think of it as hopping over one space on a number line. Each hop represents multiplying by 10 (or a power of ten, like 100 or 1000). This shift to the right makes the number larger. In the exercise, moving it once transforms 0.08 into 0.8.

• Remember: One move to the right for each 10 you're multiplying by.
• Make sure there's a space for each hop!

Now let's see what magic numbers can perform with powers of ten.

Powers of Ten

The powers of ten are like magical multipliers. They make your job with numbers easier, especially in multiplication and division. When you multiply by 10, 100, 1000, and so on, these are powers of ten.
Each power of ten increases the number of zeros following the digit 1. So, 10 is the first power of ten, 100 is the second, and so on. In maths speak:

• 10 is 10¹
• 100 is 10²
• 1000 is 10³

When multiplying a decimal like 0.08 by any power of ten, the decimal point moves to the right as many times as there are zeros. Understanding this helps in quickly calculating products without complex computations.

Place Value

Place value gives each digit in a number its own importance based on its position. This concept is crucial when you're moving decimal points or working with decimals, as it helps us understand numbers like 0.08 properly.
In 0.08, the 8 is in the "hundredths" place, meaning it's 8 parts out of 100. When you multiply by powers of ten, like 10 in our exercise, the place value changes. Let's shift our attention to the practical impact:

• 0.08: The 8 is in the hundredths place.
• 0.8: After moving the decimal point one place, the 8 moves to the "tenths" place.

Hence, understanding place value ensures smooth sailing through decimals, positioning digits correctly after moving the decimal.

Multiplication Steps

Grasping multiplication steps for decimals can transform a seemingly complicated process into a simple routine. Consider the series of steps used in the original exercise:
1. **Understand the Problem:** Identify numbers and determine how many decimal places are involved.
2. **Identify the Initial Decimal Position:** Pinpoint where the decimal currently sits.
3. **Move the Decimal Point:** Shift it to the right for multiplication. Count spaces based on the power of ten.
4. **Result of the Multiplication:** Write down the final number reflecting the new position of the decimal.
These steps act as a handy guide to manage your decimal number operations efficiently. With practice, they become second nature, bringing clarity and precision into your arithmetic life.