Here are the answers for each number based on the rules of significant digits.
Rules to remember:
1.
Non-zero numbers (1-9) are always significant.
2.
Zeros between non-zero numbers are significant (e.g., in 3007).
3.
Leading zeros (zeros at the start, like 0.005) are
never significant; they just show where the decimal point is.
4.
Trailing zeros (zeros at the end) are significant
only if there is a decimal point. If there is no decimal point (like in 520 or 7000), they are usually not considered significant unless specified otherwise.
5. In
scientific notation (like $4 \times 10^{-6}$), only look at the number part before the "x". The power of 10 does not count.
Step-by-step Solution:
1)
0.00180: The leading zeros don't count. The '1' and '8' count. The zero at the end counts because there is a decimal point. (3 digits: 1, 8, 0)
2)
$4 \times 10^{-6}$: Look only at the '4'. (1 digit)
3)
3007: All non-zeros count. The zeros are sandwiched in the middle, so they count too. (4 digits: 3, 0, 0, 7)
4)
0.00120: Leading zeros don't count. '1' and '2' count. The final zero counts because of the decimal point. (3 digits: 1, 2, 0)
5)
8096: All digits are non-zero or sandwiched zeros. (4 digits)
6)
49.418: All digits are non-zero. (5 digits)
7)
$6 \times 10^{-8}$: Look only at the '6'. (1 digit)
8)
$1 \times 10^{-7}$: Look only at the '1'. (1 digit)
9)
7000: There is no decimal point, so the trailing zeros do not count. Only the '7' is significant. (1 digit)
10)
8780: No decimal point, so the trailing zero doesn't count. (3 digits: 8, 7, 8)
11)
520: No decimal point, so the trailing zero doesn't count. (2 digits: 5, 2)
12)
0.0077: Leading zeros don't count. The two '7's count. (2 digits)
13)
$3.219 \times 10^4$: Look at 3.219. All four digits count. (4 digits)
14)
$6.692 \times 10^{-1}$: Look at 6.692. All four digits count. (4 digits)
15)
0.980: The '9' and '8' count. The final zero counts because of the decimal point. (3 digits)
16)
200: No decimal point, so the zeros don't count. (1 digit: 2)
17)
0.073: Leading zeros don't count. '7' and '3' count. (2 digits)
18)
0.542: The leading zero doesn't count. '5', '4', and '2' count. (3 digits)
19)
$8.0 \times 10^2$: Look at 8.0. The zero counts because it is written explicitly in scientific notation. (2 digits)
20)
3052: All digits count (sandwiched zero). (4 digits)
Final Answer:
1) 3
2) 1
3) 4
4) 3
5) 4
6) 5
7) 1
8) 1
9) 1
10) 3
11) 2
12) 2
13) 4
14) 4
15) 3
16) 1
17) 2
18) 3
19) 2
20) 4
Parent Tip: Review the logic above to help your child master the concept of basic skill math worksheet.
