Math  /  Numbers & Operations

Question8.5×$99.99=8.5 \times \$ 99.99= $91.49\$ 91.49 $108.49\$ 108.49 $11.76\$ 11.76 584992

Studdy Solution

STEP 1

What is this asking? We need to multiply 8.58.5 by $99.99\$99.99 and pick the correct answer from the choices. Watch out! Don't forget to consider the decimal places when multiplying, and make sure the units make sense!
We're dealing with dollars here.

STEP 2

1. Round and estimate
2. Precise calculation
3. Check against the estimate

STEP 3

Let's **round** $99.99\$99.99 to $100\$100 to make the multiplication easier.
This is a great way to get a quick estimate!

STEP 4

Now, we **multiply** our rounded value by 8.58.5: 8.5$100=$8508.5 \cdot \$100 = \$850 So, our **estimate** is $850\$850.
This gives us a ballpark figure and helps us catch any major errors later.

STEP 5

Let's **multiply** 8.58.5 by $99.99\$99.99 precisely: 8.5$99.998.5 \cdot \$99.99

STEP 6

We can rewrite 8.58.5 as (8+0.5)(8 + 0.5) and distribute the multiplication: (8+0.5)$99.99=(8$99.99)+(0.5$99.99)(8 + 0.5) \cdot \$99.99 = (8 \cdot \$99.99) + (0.5 \cdot \$99.99)

STEP 7

Now, let's **calculate** each part: 8$99.99=$799.928 \cdot \$99.99 = \$799.92 0.5$99.99=12$99.99=$49.9950.5 \cdot \$99.99 = \frac{1}{2} \cdot \$99.99 = \$49.995

STEP 8

**Add** these two results together: $799.92+$49.995=$849.915\$799.92 + \$49.995 = \$849.915

STEP 9

Since we're dealing with money, we **round** to two decimal places: $849.915$849.92\$849.915 \approx \$849.92

STEP 10

Our precise answer is $849.92\$849.92, and our estimate was $850\$850.
These are very close, which gives us confidence in our calculation!
The small difference is expected because we rounded $99.99\$99.99 up to $100\$100 in our estimate.

STEP 11

The correct answer is $849.92\$849.92.
Since this isn't one of the provided options, we can confidently say none of the provided answers are correct!

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