Solve Decimal Division: 1.6 ÷ 0.2 Step-by-Step Solution

Decimal Division with Multiplying by Powers of Ten

1.6:0.2= 1.6:0.2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll multiply each factor by 10, to make it easier to divide
00:21 We'll divide between the new numbers and calculate the quotient
00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1.6:0.2= 1.6:0.2=

2

Step-by-step solution

To solve the problem 1.6÷0.2 1.6 \div 0.2 , we will eliminate the decimals by converting the numbers into whole numbers and performing the division.

  • Step 1: Convert the decimals to whole numbers. Multiply both 1.6 and 0.2 by 10 to remove the decimal places.
    1.6×10=16 1.6 \times 10 = 16 and 0.2×10=2 0.2 \times 10 = 2 .
  • Step 2: Perform integer division. Now divide the two whole numbers obtained:
    16÷2=8 16 \div 2 = 8 .
  • Step 3: Verify the result. Verify by direct division using decimals:
    Perform 1.6÷0.2 1.6 \div 0.2 which is equivalent to 162=8\frac{16}{2} = 8.

The calculation confirms that our approach is correct, ensuring accuracy both in removing decimals and dividing.

Therefore, the solution to 1.6÷0.2 1.6 \div 0.2 is 8 8 .

3

Final Answer

8 8

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply both numbers by same power of ten to eliminate decimals
  • Technique: Convert 1.6÷0.2 1.6 ÷ 0.2 to 16÷2=8 16 ÷ 2 = 8 by multiplying by 10
  • Check: Verify by thinking 0.2×8=1.6 0.2 × 8 = 1.6 using multiplication ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying only the dividend by 10
    Don't multiply just 1.6 by 10 and leave 0.2 unchanged = 16÷0.2=80 16 ÷ 0.2 = 80 ! This changes the value of the division completely. Always multiply both numbers by the same power of ten to maintain the correct quotient.

Practice Quiz

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Solve the following exercise:

22.1-12.0

FAQ

Everything you need to know about this question

Why do we multiply both numbers by 10?

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Multiplying both the dividend (1.6) and divisor (0.2) by the same number keeps the answer unchanged! Think of it like 1620=1.62.0 \frac{16}{20} = \frac{1.6}{2.0} - the ratio stays the same.

What if the decimals have different numbers of decimal places?

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Find the number with more decimal places and multiply both numbers by that power of 10. For example, if you have 1.25 ÷ 0.5, multiply both by 100 to get 125 ÷ 50.

Can I just move the decimal points instead?

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Yes! Moving the decimal point right is the same as multiplying by 10. Just make sure you move the decimal point the same number of places in both numbers.

How do I know how many places to multiply by 10?

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Count the decimal places in both numbers. In 1.6÷0.2 1.6 ÷ 0.2 , both have 1 decimal place, so multiply by 10¹ = 10. If one had 2 places, you'd multiply by 100.

What if my answer is still a decimal?

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That's totally normal! Some divisions naturally result in decimals. Just make sure you've simplified correctly and check your work by multiplying back.

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