Placing the decimal point correctly in the product of 29.3 x 3.66:
To find the correct placement of the decimal in \( 107238 \), we determine how many decimal places are in the factors:
- \( 29.3 \) has 1 decimal place.
- \( 3.66 \) has 2 decimal places.
So in total, we have \( 1 + 2 = 3 \) decimal places to account for in the product \( 107238 \).
Placing the decimal point three places from the right gives us \( 107.238 \). So the correct option from the choices given is to place the decimal point between 2 and 3, which makes it 107.238.
Answer: Place the decimal point between 2 and 3.
Identifying equivalent expressions:
We need to simplify and find equivalent forms for the expression \( 8 \times 756 \times \frac{1}{100} \times \frac{1}{100} \).
Calculating:
- \( \frac{1}{100} \times \frac{1}{100} = \frac{1}{10000} \)
- Thus, the expression becomes \( 8 \times 756 \times \frac{1}{10000} \).
We can also express this as \( \frac{8 \times 756}{10000} \).
Now let's analyze the options given:
- \( 8 \times 756 \times \frac{1}{100} \times \frac{1}{100} – This is the same as ( 8 \times 756 \times \frac{1}{10000} \). (Equivalent)
- \( 8 \times 1/10 \times 756 \times \frac{1}{100} - This equals ( 8 \times 756 \times \frac{1}{1000} \), which is not equivalent.
- \( 8 \times 756 \times 10 \times 100 \) - This results in a much larger product, thus not equivalent.
- \( 8 \times 756 \times \frac{1}{10} \times \frac{1}{100} - This equals ( 8 \times 756 \times \frac{1}{1000} \), which is not equivalent.
Thus, the only equivalent expression is:
Answer: \( 8 \times 756 \times \frac{1}{100} \times \frac{1}{100} \).
Finding the product of 6,310.7: This seems like a typographical error. Assuming you meant to find the value of \( 6,310.7 \) expressed in standard numerical forms, we take it as it is:
Answer: 6,310.7 (This representation is clear without further operations).
Calculating Juanita's earnings:
Juanita earns $8.75 per hour and works for 23 hours.
Calculating her total earnings:
\[ 8.75 \times 23 = 201.25 \]
Thus, her total earnings are:
Answer: $201.25.
Estimating the product by rounding to the nearest ten:
Let's assume the numbers are \( 29.3 \) and \( 3.66 \):
- Rounding \( 29.3 \) gives us approximately 30.
- Rounding \( 3.66 \) gives us approximately 4.
Now, let's find the estimated product:
\[ 30 \times 4 = 120 \]
Therefore, rounding the numbers and calculating gives us:
Answer: Estimated product is approximately 120.