Scientific Notation ⇄ Decimal Converter
Bidirectional Converter
Coefficient
× 10
Exponent
Understanding Scientific Notation to Decimal Conversion
Converting scientific notation to decimal notation (also called standard form or decimal notation without exponents) is a fundamental mathematical skill. Scientific notation expresses numbers as a coefficient multiplied by a power of 10, like \( 2 \times 10^5 \). Converting to decimal notation means writing the number without exponents, showing its full value. This process is essential for understanding calculator displays, scientific data, and real-world measurements.
Why Learn These Conversions?
- Calculator understanding: Interpret scientific calculator displays (Casio fx-991ex, etc.)
- Data interpretation: Understand scientific measurements and statistics
- Homework solutions: Required for showing work in standard form
- Real-world numbers: Convert between compact and expanded forms
- Testing requirements: Needed for standardized tests and exams
- Professional applications: Essential in science, engineering, finance
How to Convert Scientific Notation to Decimal
📐 The Simple Rule
\( a \times 10^n \) → Move decimal point \( n \) places
Positive exponent: Move decimal point \( n \) places to the RIGHT
Negative exponent: Move decimal point \( n \) places to the LEFT
Zero exponent: Number stays the same (10⁰ = 1)
Example 1: 2×10⁵ in Decimal Notation
Converting \( 2 \times 10^5 \) to Decimal
Scientific Notation: \( 2 \times 10^5 \)
Step 1: Exponent is +5 (positive), so move decimal 5 places RIGHT
Step 2: Start with 2.0 and move decimal: 2.0 → 20 → 200 → 2,000 → 20,000 → 200,000
Decimal Notation: 200,000
Example 2: Decimal Notation of 2.3×10⁷
Converting \( 2.3 \times 10^7 \) to Decimal
Scientific Notation: \( 2.3 \times 10^7 \)
Step 1: Exponent is +7, so move decimal 7 places RIGHT
Step 2: Start with 2.3 → 23 → 230 → 2,300 → 23,000 → 230,000 → 2,300,000 → 23,000,000
Decimal Notation: 23,000,000
Example 3: Negative Exponent
Converting \( 4.5 \times 10^{-3} \) to Decimal
Scientific Notation: \( 4.5 \times 10^{-3} \)
Step 1: Exponent is -3 (negative), so move decimal 3 places LEFT
Step 2: Start with 4.5 → 0.45 → 0.045 → 0.0045
Decimal Notation: 0.0045
How to Convert Decimal to Scientific Notation
📐 Reverse Conversion Rule
Step 1: Move decimal to create a number between 1 and 10
Step 2: Count how many places you moved
Step 3: If moved LEFT, exponent is positive; if moved RIGHT, exponent is negative
Step 4: Write as coefficient × 10^exponent
Example: 450,000 to Scientific Notation
Converting 450,000 to Scientific Notation
Decimal: 450,000
Step 1: Move decimal to get 4.5 (between 1 and 10)
Step 2: Moved decimal 5 places LEFT (450000. → 4.50000)
Step 3: Moved left means positive exponent: +5
Scientific Notation: \( 4.5 \times 10^5 \)
Using Casio fx-991EX Scientific Calculator
Converting Scientific Notation to Decimal on Casio fx-991EX
Method 1 - Using S⇔D Function:
1. Enter the number in scientific notation
2. Press [SHIFT] then [=] (displays S⇔D)
3. The calculator toggles between scientific and decimal display
Method 2 - Change Display Setting:
1. Press [SHIFT] [SETUP] (Menu)
2. Navigate to "Display" settings
3. Select "Norm" for normal decimal display
4. Choose Norm 1 (shows decimals for most numbers) or Norm 2
Example on Calculator:
Enter: 2 × 10^5
Type: 2 [×] 10 [^] 5 [=]
Result shows: 200000 (in decimal) or 2×10⁵ (in scientific)
Toggle with [SHIFT] [=]
Frequently Asked Questions
How do you convert 2×10⁵ to decimal notation?
To convert 2×10⁵ to decimal notation: the exponent 5 means move the decimal point 5 places to the right. Start with 2.0 and move: 2.0 → 20 → 200 → 2,000 → 20,000 → 200,000. The decimal notation is 200,000.
What is the decimal notation of 2.3×10⁷?
The decimal notation of 2.3×10⁷ is 23,000,000. Move the decimal point 7 places right: 2.3 → 23 → 230 → 2,300 → 23,000 → 230,000 → 2,300,000 → 23,000,000. This represents twenty-three million in standard form.
How do you write decimal notation without the use of exponents?
To write decimal notation without the use of exponents, convert scientific notation by moving the decimal point: for positive exponents, move right and add zeros as needed; for negative exponents, move left and add leading zeros. Example: 5×10³ = 5,000 (no exponents shown).
How do you convert scientific notation to decimal notation?
To convert scientific notation to decimal notation: (1) Look at the exponent on 10, (2) If positive, move decimal right that many places, (3) If negative, move decimal left that many places, (4) Add zeros as needed. Example: 3.7×10⁴ = 37,000 (moved 4 places right).
How do you convert decimal to scientific notation?
To convert decimal to scientific notation: (1) Move decimal to create a number between 1 and 10, (2) Count places moved, (3) If moved left, exponent is positive; if moved right, exponent is negative, (4) Write as coefficient × 10^exponent. Example: 6,500 = 6.5×10³ (moved 3 left).
How do I convert scientific notation to decimal on a Casio fx-991EX?
On the Casio fx-991EX scientific notation to decimal conversion: press [SHIFT] then [=] to toggle between formats, or change display settings via [SHIFT] [SETUP] → Display → Norm. The calculator can show results in either scientific or decimal notation.
What does a positive exponent mean when converting?
A positive exponent in scientific notation to decimal conversion means the number is large (≥10). Move the decimal point to the RIGHT. Example: 10² means move 2 right, so 1.0 becomes 100. Each positive power of 10 makes the number 10 times larger.
What does a negative exponent mean when converting?
A negative exponent means the number is small (<1). Move the decimal point to the LEFT. Example: 10⁻³ means move 3 left, so 5.0 becomes 0.005. Each negative power of 10 makes the number 10 times smaller. This creates decimal notation with leading zeros.
How many zeros do I add when converting?
When converting scientific notation to decimal, add zeros to fill the spaces as you move the decimal. For 3×10⁵, you move 5 places right from 3.0: need to add 4 zeros to get 300,000. For 2×10⁻⁴, move 4 left from 2.0: add 3 zeros for 0.0002.
Is standard form the same as decimal notation?
Yes, decimal notation without exponents is also called standard form or ordinary decimal notation. It's the regular way of writing numbers without powers of 10. For example, 250,000 is standard/decimal form, while 2.5×10⁵ is scientific notation. Both represent the same value.
Quick Reference Table
| Scientific Notation | Decimal Notation | In Words |
|---|---|---|
| \( 2 \times 10^5 \) | 200,000 | Two hundred thousand |
| \( 2.3 \times 10^7 \) | 23,000,000 | Twenty-three million |
| \( 5 \times 10^3 \) | 5,000 | Five thousand |
| \( 7.5 \times 10^{-2} \) | 0.075 | Seventy-five thousandths |
| \( 3.2 \times 10^{-4} \) | 0.00032 | Thirty-two ten-thousandths |
