Math  /  Numbers & Operations

Question8. Select the correct quotient. 0.01224÷0.00180.01224 \div 0.0018 06.80 6.7 6.8 06.8

Studdy Solution

STEP 1

What is this asking? We need to divide a small decimal number, 0.01224, by another even smaller decimal number, 0.0018, and pick the correct answer from the choices. Watch out! Don't rush!
It's easy to misplace the decimal when dividing by decimals.
Also, pay close attention to the number of significant digits in the answer choices.

STEP 2

1. Set up the division
2. Divide carefully
3. Match the format

STEP 3

Alright, let's **rewrite** this division problem as a fraction!
This makes it easier to see what we're dealing with: 0.012240.0018\frac{0.01224}{0.0018}

STEP 4

Now, we want to get rid of those pesky decimals in the **denominator**.
We can do this by multiplying both the **numerator** and the **denominator** by a suitable power of 10.
Since there are four decimal places in the denominator, we'll multiply by 1000010000\frac{10000}{10000}, which is the same as multiplying by **one**! 0.012240.00181000010000\frac{0.01224}{0.0018} \cdot \frac{10000}{10000}

STEP 5

This gives us: 0.01224100000.001810000=122.418\frac{0.01224 \cdot 10000}{0.0018 \cdot 10000} = \frac{122.4}{18} Much better!
Now we have a division problem we can tackle more easily.

STEP 6

Let's perform the division: 122.418\frac{122.4}{18} We can think of this as: How many times does 18 go into 122.4?

STEP 7

We can perform long division or use a calculator.
Let's do a quick long division! <br/>6.818122.41081441440\begin{array}{cc}<br />6. & 8 \\ 18 & 122.4 \\ 108 & \\ 14 & 4 \\ 14 & 4 \\ 0 & \end{array}

STEP 8

So, 122.4÷18=6.8122.4 \div 18 = 6.8.
Awesome!

STEP 9

Looking back at our answer choices, we see **6.8**.
That matches our result perfectly!

STEP 10

The correct quotient is 6.8.

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