To convert scientific notation to standard form, move the decimal point in the coefficient by the number of places the exponent shows — right for a positive exponent, left for a negative one — and fill any empty places with zeros. For example, 5.27 × 10^4 = 52,700 and 1.5 × 10^-3 = 0.0015.
Converting back is the reverse of writing a number in scientific notation, and it uses the same single idea: the exponent is a count of decimal-point moves. The only new skill is filling empty places with zeros when the point runs out of digits — which is where most mistakes happen. Below is the two-step method, worked examples in both directions of the exponent, the zero-filling walkthrough, and the E-notation decode.
What “Standard Form” Means Here
Standard form is the ordinary way of writing a number: 52,700, 0.0015, 1,000,800, 149,600,000. Scientific notation is the same number written as a coefficient between 1 and 10 times a power of 10: 5.27 × 10^4, 1.5 × 10^-3, 1.0008 × 10^6, 1.496 × 10^8. Converting between the two changes nothing about the value — it only changes how the zeros are shown. (One naming warning: in the UK, “standard form” is the name for scientific notation itself, so check which meaning your textbook uses before an exam.)
Check any conversion instantly with a free scientific notation calculator, which shows the decimal-point moves step by step.
The 2-Step Method
Step 1: Read the exponent — it tells you the direction and the distance.
A positive exponent means the number is bigger than the coefficient, so the decimal point moves right. A negative exponent means the number is smaller than the coefficient, so the point moves left. The exponent’s size is the number of places: 10^4 means 4 places, 10^-3 means 3 places.
Step 2: Move the point and fill empty places with zeros.
Move the decimal point the required number of places. When the point runs past the last digit, write a zero in each empty place. When it runs before the first digit, write “0.” and then the zeros. Then drop the × 10^n — the number you have left is the standard form.
Worked Example: Positive Exponent (Move Right)
Worked example: write 5.27 × 10^4 in standard form.
- Read the exponent. It is +4, so move the decimal point 4 places to the right.
- Start with the coefficient. 5.27 — the point sits after the 5.
- Move it. One place right: 52.7. Two places: 527. The digits have run out, so fill with zeros: three places: 5,270. Four places: 52,700.
- Write the answer: 5.27 × 10^4 = 52,700.
More positive-exponent conversions, worked the same way: 1.0008 × 10^6 → the point moves 6 places right → 1,000,800. 4.673 × 10^4 → 46,730. 1.61 × 10^4 → 16,100. 5.56 × 10^4 → 55,600. 1.86 × 10^7 → 18,600,000. And 1.496 × 10^8 km → 149,600,000 km, the Earth–Sun distance. Notice the pattern: a positive exponent of n always produces a number with n digits after the first one — the zeros you filled in are exactly the exponent doing its job.
Worked Example: Negative Exponent (Move Left)
Worked example: write 1.5 × 10^-3 in standard form.
- Read the exponent. It is −3, so move the decimal point 3 places to the left.
- Start with the coefficient. 1.5 — the point sits after the 1.
- Move it. One place left: 0.15. Two places: 0.015. Three places: 0.0015 — the point has run past the first digit, so a zero fills the empty place.
- Write the answer: 1.5 × 10^-3 = 0.0015.
More negative-exponent conversions: 4.5 × 10^-2 → 0.045. 1.25 × 10^-4 → 0.000125. 3.20 × 10^-9 → 0.0000000032. 6.88 × 10^-12 → 0.00000000000688. And the famous one: 4.5 × 10^-9 → 0.0000000045 — the number from the video hook, nine places left, eight zeros then the 45. A free scientific notation calculator shows each of these moves, so you can watch the zeros appear one at a time.
The Zero-Counting Shortcut
You can predict the zeros before you move anything:
- Positive exponent n: the standard form has n digits after the first digit. 5.27 × 10^4 has 4 digits after the 5 (2, 7, 0, 0) → 52,700. 1.0008 × 10^6 has 6 digits after the 1 → 1,000,800.
- Negative exponent −n: the standard form starts with “0.”, then (n − 1) zeros, then the coefficient’s digits. 1.5 × 10^-3 starts with “0.”, then 2 zeros, then 15 → 0.0015. 4.5 × 10^-9 starts with “0.”, then 8 zeros, then 45 → 0.0000000045.
If your answer has the wrong number of zeros, the exponent was miscounted — count again from the shortcut, not from the moves.
Converting E-Notation to a Normal Number
Calculators, spreadsheets and code do not print × 10^n — they print E-notation, where E means “times 10 to the power of”. 4.5E-9 is 4.5 × 10^-9 = 0.0000000045, and 2.99792458E8 is 2.99792458 × 10^8 = 299,792,458. Read the number after the E exactly as an exponent and apply the same two steps: 1.496E8 → the point moves 8 places right → 149,600,000. 6.02E23 → the point moves 23 places right → 602,000,000,000,000,000,000,000, Avogadro’s number. The minus sign after the E belongs to the exponent — 4.5E-9 is a tiny number, while 4.5E9 is 4,500,000,000. Mixing those two up is the same sign-flip trap as writing 4.5 × 10^9 for 0.0000000045, and the size check catches it the same way.
Both Directions, Side by Side
| Scientific notation | Move the point | Standard form |
|---|---|---|
| 5.27 × 10^4 | 4 places right | 52,700 |
| 1.0008 × 10^6 | 6 places right | 1,000,800 |
| 4.673 × 10^4 | 4 places right | 46,730 |
| 1.61 × 10^4 | 4 places right | 16,100 |
| 1.496 × 10^8 | 8 places right | 149,600,000 |
| 1.5 × 10^-3 | 3 places left | 0.0015 |
| 4.5 × 10^-2 | 2 places left | 0.045 |
| 1.25 × 10^-4 | 4 places left | 0.000125 |
| 3.20 × 10^-9 | 9 places left | 0.0000000032 |
| 4.5 × 10^-9 | 9 places left | 0.0000000045 |
Read any row backwards and it is the forward conversion: 52,700 → the point moves 4 places left → 5.27 × 10^4. The two directions are one rule read in opposite directions, which is why learning to convert back also teaches you to write numbers in scientific notation in the first place.
4 Mistakes That Cost Marks
1. Moving the point the wrong way. A positive exponent moves the point right (the number gets bigger); a negative exponent moves it left (the number gets smaller). 5.27 × 10^4 is 52,700, not 0.000527 — if your answer is smaller than your coefficient while the exponent is positive, you moved the wrong way.
2. Forgetting to fill empty places with zeros. 1.0008 × 10^6 is 1,000,800, not 1.0008 with the point just “moved” — every place the point passes needs a digit, and zeros fill the gaps. Count the digits after the first one: there must be exactly n of them for an exponent of n.
3. Dropping the coefficient’s trailing zeros. 3.20 × 10^-9 is 0.0000000032, and the trailing zero in 3.20 is a significant figure — it says the measurement is precise to three figures. Writing 0.000000003 loses that information, and on a lab report it loses the mark.
4. Reading E-notation backwards. 4.5E-9 means 4.5 × 10^-9 = 0.0000000045, not 4.5 × 10^9. The minus sign after the E belongs to the exponent. On a calculator display, E-9 is a tiny number; E9 is a huge one. The logarithm calculator shows the same power-of-10 thinking from the other side: log10(1000) = 3, because 1000 = 10^3.
Frequently Asked Questions
How do you convert scientific notation to standard form?
Move the decimal point in the coefficient by the number of places the exponent shows: right for a positive exponent, left for a negative one, filling empty places with zeros. 5.27 × 10^4 = 52,700 and 1.5 × 10^-3 = 0.0015.
What is 5.27 × 10^4 in standard form?
52,700. The exponent is +4, so the decimal point moves 4 places to the right from 5.27: 52.7, 527, 5,270, 52,700.
What is 1.5 × 10^-3 in standard form?
0.0015. The exponent is −3, so the decimal point moves 3 places to the left from 1.5: 0.15, 0.015, 0.0015.
How do you convert E-notation to a normal number?
Read the number after the E as the exponent and apply the same rule: 4.5E-9 = 4.5 × 10^-9 = 0.0000000045, and 2.99792458E8 = 299,792,458. The E means “times 10 to the power of”.
What is 6.02 × 10^23 in standard form?
602,000,000,000,000,000,000,000 — Avogadro’s number, the number of particles in one mole. The exponent is +23, so the point moves 23 places right, filling 21 places with zeros after the digits 602.
How do you know which way to move the decimal point?
By the exponent’s sign: positive means right (the number gets bigger than the coefficient), negative means left (it gets smaller). Check by size — if your answer is bigger than 1 while the exponent is negative, you moved the wrong way.
Keep Practicing
Work these by hand and verify with the free scientific notation calculator: 4.673 × 10^4 = 46,730; 1.61 × 10^4 = 16,100; 5.56 × 10^4 = 55,600; 1.86 × 10^7 = 18,600,000; 4.5 × 10^-2 = 0.045; 1.25 × 10^-4 = 0.000125; and 3.20 × 10^-9 = 0.0000000032.