Question

Column A	Column B
\((0.01)(0.07)(70)\)	\(0.49\)

Hint:

When multiplying by powers of 10, move the decimal point. For example, multiplying \( (0.01)(70) \) first gives \(0.7\). Then \(0.7 \times 0.07 = 0.049\). Rearranging the multiplication order can sometimes simplify the calculation.

Answer 1

Step 1: Understanding the Concept:
The problem involves multiplying decimals and a whole number. It tests understanding of decimal place values.
Step 2: Key Formula or Approach:
To multiply decimals, one can convert them to fractions or multiply them as whole numbers and then place the decimal point correctly in the result.
Step 3: Detailed Explanation:
For Column A:
The expression is \((0.01)(0.07)(70)\).
Let's multiply the decimals first: \(0.01 \times 0.07\).
\(1 \times 7 = 7\). The first number has 2 decimal places and the second has 2, so the product will have \(2+2=4\) decimal places.
So, \(0.01 \times 0.07 = 0.0007\).
Now, multiply this by 70:
\[ 0.0007 \times 70 \] This is the same as \(0.0007 \times 7 \times 10\).
\(0.0007 \times 7 = 0.0049\).
\(0.0049 \times 10 = 0.049\).
Alternatively, using fractions:
\[ \left(\frac{1}{100}\right) \times \left(\frac{7}{100}\right) \times 70 = \frac{1 \times 7 \times 70}{100 \times 100} = \frac{490}{10000} = \frac{49}{1000} = 0.049 \] The value of Column A is 0.049.
For Column B:
The value is 0.49.
Step 4: Final Answer:
Comparing the two values:
Column A = 0.049
Column B = 0.49
To compare, we can write them with the same number of decimal places: 0.049 and 0.490. It is clear that \(49<490\), so \(0.049<0.49\).
Therefore, the quantity in Column B is greater.