Final answer:
The digit 4 has a greater value in the number 0.04 than in 0.004 because it is ten times as much, due to its place value in the hundredths place compared to the thousandths place.
Step-by-step explanation:
When looking at the numbers 0.04 and 0.004, the digit 4 has greater value in the number 0.04 because of its place value. In the number 0.04, the 4 is in the hundredths place (10-2), which means it is equivalent to 4/100 or 0.04. On the other hand, in the number 0.004, the 4 is in the thousandths place (10-3), which makes it equivalent to 4/1000 or 0.004.
The value of 4 in 0.04 is ten times as much as its value in 0.004, since moving one decimal place to the left multiplies the value of the digit by 10. To visualize this, you could rewrite 0.04 as 4 x 10-2 and 0.004 as 4 x 10-3. The exponent change from -2 to -3 indicates that the latter is ten times smaller.