Solve: Locating the Decimal Point in 2.35 × 7.6 = 1786

Q: Why do I add the decimal places instead of multiplying them?

When multiplying decimals, you add the number of decimal places because each decimal place represents a power of 10. Think of it like adding exponents: $ 10^{-2} \times 10^{-1} = 10^{-3} $.

Q: What if I get a different number when I multiply 235 × 76?

You should get 17,860, not 1786. The problem gives 1786 as the digits without proper decimal placement. Your job is to figure out where the decimal point goes!

Q: How can I check if 17.86 is reasonable?

Use estimation! Round 2.35 to 2 and 7.6 to 8. Since $ 2 \times 8 = 16 $, an answer around 17.86 makes perfect sense.

Q: What if the problem had more decimal places?

The same rule applies! If you had 2.135 × 7.62, that would be 3 + 2 = 5 decimal places in your final answer. Always count and add them up.

Q: Can I move the decimal point a different way?

No! The decimal placement is determined by the rule. You can't just move it to make the answer 'look right' - mathematics has specific rules we must follow.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert decimal numbers to fractions

00:07 Write the number as a whole number in the numerator, and a power of 10 in the denominator

00:10 Add zeros to the denominator according to the number of digits after the decimal point

00:17 Move to the second factor, use the same method

00:30 Make sure to multiply numerator by numerator and denominator by denominator

00:39 Calculate the multiplications

00:49 Now write the numerator as a whole number

00:56 For the number of zeros in the denominator, position the decimal point

01:03 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

Given the following exercise, find the correct place of the decimal point:

$2.35\times7.6=1786$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the decimal places in each number.
Step 2: Determine the total number of decimal places needed in the product.
Step 3: Adjust the product to include the correct number of decimal places.
Step 4: Select the correct answer from the choices based on this calculation.

Let's work through these steps:

Step 1: The number $2.35$ has two decimal places, and the number $7.6$ has one decimal place. This gives us a total of $2 + 1 = 3$ decimal places needed in the product.

Step 2: Multiply the numbers as whole numbers: $235 \times 76 = 17860$ . Notice it seems like $1786$ in the problem statement, which lacks correct decimal placement.

Step 3: With a total of three decimal places needed in the result, we place the decimal point in $1786$ to make it $17.86$ , adding those three decimal places.

Step 4: Compare this with the given options. The placement in option 2 is $\text{\textbf{17.86}}$ , which correctly reflects the required three decimal places.

Therefore, the correct solution is $17.86$ .

3

Final Answer

$17.86$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total decimal places in both factors to determine product placement
Technique: Add decimal places: 2.35 (2 places) + 7.6 (1 place) = 3 total places
Check: Verify 17.86 makes sense: 2 × 8 = 16, so 17.86 is reasonable ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count decimal places in both numbers
Don't just count one number's decimal places = wrong placement like 178.6 instead of 17.86! This ignores half the information needed for proper decimal positioning. Always count decimal places in BOTH numbers and add them together.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 0.008 =$

FAQ

Everything you need to know about this question

Why do I add the decimal places instead of multiplying them?

+

When multiplying decimals, you add the number of decimal places because each decimal place represents a power of 10. Think of it like adding exponents: $10^{-2} \times 10^{-1} = 10^{-3}$ .

What if I get a different number when I multiply 235 × 76?

+

You should get 17,860, not 1786. The problem gives 1786 as the digits without proper decimal placement. Your job is to figure out where the decimal point goes!

How can I check if 17.86 is reasonable?

+

Use estimation! Round 2.35 to 2 and 7.6 to 8. Since $2 \times 8 = 16$ , an answer around 17.86 makes perfect sense.

What if the problem had more decimal places?

+

The same rule applies! If you had 2.135 × 7.62, that would be 3 + 2 = 5 decimal places in your final answer. Always count and add them up.

Can I move the decimal point a different way?

+

No! The decimal placement is determined by the rule. You can't just move it to make the answer 'look right' - mathematics has specific rules we must follow.

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Solve: Locating the Decimal Point in 2.35 × 7.6 = 1786

Decimal Multiplication with Place Value Positioning

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