Math worksheet for converting standard form numbers to expanded exponential form.

To convert a number from standard form to expanded exponential form, we look at the place value of each digit. We write each digit multiplied by its place value expressed as a power of 10.

The powers of 10 correspond to the position of the digit:
- Ones place: $10^0$
- Tens place: $10^1$
- Hundreds place: $10^2$
- Thousands place: $10^3$
- Ten thousands place: $10^4$
- Hundred thousands place: $10^5$
- Millions place: $10^6$
- Ten millions place: $10^7$
- Hundred millions place: $10^8$

Let's solve each problem step-by-step.

1. 220,732,073
- The first 2 is in the hundred millions place ($10^8$).
- The second 2 is in the ten millions place ($10^7$).
- The 0 in the millions place is usually skipped in expanded form unless required, but typically we only write non-zero digits. Let's stick to non-zero digits for clarity, which is standard for this type of worksheet.
- The 7 is in the hundred thousands place ($10^5$).
- The 3 is in the ten thousands place ($10^4$).
- The 2 is in the thousands place ($10^3$).
- The 0 in the hundreds place is skipped.
- The 7 is in the tens place ($10^1$).
- The 3 is in the ones place ($10^0$).

Result: $(2 \times 10^8) + (2 \times 10^7) + (7 \times 10^5) + (3 \times 10^4) + (2 \times 10^3) + (7 \times 10^1) + (3 \times 10^0)$

2. 358,837,642
- 3 is in the hundred millions place ($10^8$).
- 5 is in the ten millions place ($10^7$).
- 8 is in the millions place ($10^6$).
- 8 is in the hundred thousands place ($10^5$).
- 3 is in the ten thousands place ($10^4$).
- 7 is in the thousands place ($10^3$).
- 6 is in the hundreds place ($10^2$).
- 4 is in the tens place ($10^1$).
- 2 is in the ones place ($10^0$).

Result: $(3 \times 10^8) + (5 \times 10^7) + (8 \times 10^6) + (8 \times 10^5) + (3 \times 10^4) + (7 \times 10^3) + (6 \times 10^2) + (4 \times 10^1) + (2 \times 10^0)$

3. 938,118,409
- 9 is in the hundred millions place ($10^8$).
- 3 is in the ten millions place ($10^7$).
- 8 is in the millions place ($10^6$).
- 1 is in the hundred thousands place ($10^5$).
- 1 is in the ten thousands place ($10^4$).
- 8 is in the thousands place ($10^3$).
- 4 is in the hundreds place ($10^2$).
- 0 in tens place is skipped.
- 9 is in the ones place ($10^0$).

Result: $(9 \times 10^8) + (3 \times 10^7) + (8 \times 10^6) + (1 \times 10^5) + (1 \times 10^4) + (8 \times 10^3) + (4 \times 10^2) + (9 \times 10^0)$

4. 242,418,156
- 2 is in the hundred millions place ($10^8$).
- 4 is in the ten millions place ($10^7$).
- 2 is in the millions place ($10^6$).
- 4 is in the hundred thousands place ($10^5$).
- 1 is in the ten thousands place ($10^4$).
- 8 is in the thousands place ($10^3$).
- 1 is in the hundreds place ($10^2$).
- 5 is in the tens place ($10^1$).
- 6 is in the ones place ($10^0$).

Result: $(2 \times 10^8) + (4 \times 10^7) + (2 \times 10^6) + (4 \times 10^5) + (1 \times 10^4) + (8 \times 10^3) + (1 \times 10^2) + (5 \times 10^1) + (6 \times 10^0)$

5. 759,480,833
- 7 is in the hundred millions place ($10^8$).
- 5 is in the ten millions place ($10^7$).
- 9 is in the millions place ($10^6$).
- 4 is in the hundred thousands place ($10^5$).
- 8 is in the ten thousands place ($10^4$).
- 0 in thousands place is skipped.
- 8 is in the hundreds place ($10^2$).
- 3 is in the tens place ($10^1$).
- 3 is in the ones place ($10^0$).

Result: $(7 \times 10^8) + (5 \times 10^7) + (9 \times 10^6) + (4 \times 10^5) + (8 \times 10^4) + (8 \times 10^2) + (3 \times 10^1) + (3 \times 10^0)$

6. 743,276,246
- 7 is in the hundred millions place ($10^8$).
- 4 is in the ten millions place ($10^7$).
- 3 is in the millions place ($10^6$).
- 2 is in the hundred thousands place ($10^5$).
- 7 is in the ten thousands place ($10^4$).
- 6 is in the thousands place ($10^3$).
- 2 is in the hundreds place ($10^2$).
- 4 is in the tens place ($10^1$).
- 6 is in the ones place ($10^0$).

Result: $(7 \times 10^8) + (4 \times 10^7) + (3 \times 10^6) + (2 \times 10^5) + (7 \times 10^4) + (6 \times 10^3) + (2 \times 10^2) + (4 \times 10^1) + (6 \times 10^0)$

7. 429,700,972
- 4 is in the hundred millions place ($10^8$).
- 2 is in the ten millions place ($10^7$).
- 9 is in the millions place ($10^6$).
- 7 is in the hundred thousands place ($10^5$).
- 0s in ten thousands and thousands places are skipped.
- 9 is in the hundreds place ($10^2$).
- 7 is in the tens place ($10^1$).
- 2 is in the ones place ($10^0$).

Result: $(4 \times 10^8) + (2 \times 10^7) + (9 \times 10^6) + (7 \times 10^5) + (9 \times 10^2) + (7 \times 10^1) + (2 \times 10^0)$

8. 184,454,902
- 1 is in the hundred millions place ($10^8$).
- 8 is in the ten millions place ($10^7$).
- 4 is in the millions place ($10^6$).
- 4 is in the hundred thousands place ($10^5$).
- 5 is in the ten thousands place ($10^4$).
- 4 is in the thousands place ($10^3$).
- 9 is in the hundreds place ($10^2$).
- 0 in tens place is skipped.
- 2 is in the ones place ($10^0$).

Result: $(1 \times 10^8) + (8 \times 10^7) + (4 \times 10^6) + (4 \times 10^5) + (5 \times 10^4) + (4 \times 10^3) + (9 \times 10^2) + (2 \times 10^0)$

9. 669,713,501
- 6 is in the hundred millions place ($10^8$).
- 6 is in the ten millions place ($10^7$).
- 9 is in the millions place ($10^6$).
- 7 is in the hundred thousands place ($10^5$).
- 1 is in the ten thousands place ($10^4$).
- 3 is in the thousands place ($10^3$).
- 5 is in the hundreds place ($10^2$).
- 0 in tens place is skipped.
- 1 is in the ones place ($10^0$).

Result: $(6 \times 10^8) + (6 \times 10^7) + (9 \times 10^6) + (7 \times 10^5) + (1 \times 10^4) + (3 \times 10^3) + (5 \times 10^2) + (1 \times 10^0)$

10. 912,917,861
- 9 is in the hundred millions place ($10^8$).
- 1 is in the ten millions place ($10^7$).
- 2 is in the millions place ($10^6$).
- 9 is in the hundred thousands place ($10^5$).
- 1 is in the ten thousands place ($10^4$).
- 7 is in the thousands place ($10^3$).
- 8 is in the hundreds place ($10^2$).
- 6 is in the tens place ($10^1$).
- 1 is in the ones place ($10^0$).

Result: $(9 \times 10^8) + (1 \times 10^7) + (2 \times 10^6) + (9 \times 10^5) + (1 \times 10^4) + (7 \times 10^3) + (8 \times 10^2) + (6 \times 10^1) + (1 \times 10^0)$

Final Answer:
1. $(2 \times 10^8) + (2 \times 10^7) + (7 \times 10^5) + (3 \times 10^4) + (2 \times 10^3) + (7 \times 10^1) + (3 \times 10^0)$
2. $(3 \times 10^8) + (5 \times 10^7) + (8 \times 10^6) + (8 \times 10^5) + (3 \times 10^4) + (7 \times 10^3) + (6 \times 10^2) + (4 \times 10^1) + (2 \times 10^0)$
3. $(9 \times 10^8) + (3 \times 10^7) + (8 \times 10^6) + (1 \times 10^5) + (1 \times 10^4) + (8 \times 10^3) + (4 \times 10^2) + (9 \times 10^0)$
4. $(2 \times 10^8) + (4 \times 10^7) + (2 \times 10^6) + (4 \times 10^5) + (1 \times 10^4) + (8 \times 10^3) + (1 \times 10^2) + (5 \times 10^1) + (6 \times 10^0)$
5. $(7 \times 10^8) + (5 \times 10^7) + (9 \times 10^6) + (4 \times 10^5) + (8 \times 10^4) + (8 \times 10^2) + (3 \times 10^1) + (3 \times 10^0)$
6. $(7 \times 10^8) + (4 \times 10^7) + (3 \times 10^6) + (2 \times 10^5) + (7 \times 10^4) + (6 \times 10^3) + (2 \times 10^2) + (4 \times 10^1) + (6 \times 10^0)$
7. $(4 \times 10^8) + (2 \times 10^7) + (9 \times 10^6) + (7 \times 10^5) + (9 \times 10^2) + (7 \times 10^1) + (2 \times 10^0)$
8. $(1 \times 10^8) + (8 \times 10^7) + (4 \times 10^6) + (4 \times 10^5) + (5 \times 10^4) + (4 \times 10^3) + (9 \times 10^2) + (2 \times 10^0)$
9. $(6 \times 10^8) + (6 \times 10^7) + (9 \times 10^6) + (7 \times 10^5) + (1 \times 10^4) + (3 \times 10^3) + (5 \times 10^2) + (1 \times 10^0)$
10. $(9 \times 10^8) + (1 \times 10^7) + (2 \times 10^6) + (9 \times 10^5) + (1 \times 10^4) + (7 \times 10^3) + (8 \times 10^2) + (6 \times 10^1) + (1 \times 10^0)$