8.EE.A.3 8th Grade Expressions & Equations

Scientific Notation Conversion

Use numbers expressed in scientific notation to estimate very large or very small quantities and to compare their sizes.

How to explain it

At this standard, students convert between standard form and scientific notation for very large and very small numbers, using the direction of decimal movement to determine the sign and magnitude of the exponent.

The anchor students hold onto: Standard → SN: move the decimal until the coefficient sits between 1 and 10; count places moved (left-move gives positive exponent, right-move gives negative).

Sets up 8.EE.A.4 (Operations with Scientific Notation) by establishing fluent conversion in both directions — the prerequisite for adding, multiplying, and dividing in SN.

Worked examples

Example 1 Large → SN

47,000

Step 1Move decimal 4 places left.

Step 2Coefficient: 4.7

Step 347,000 = 4.7 × 10⁴

Answer4.7 × 10⁴

Example 2 Small → SN

0.00062

Step 1Move decimal 4 places right.

Step 2Coefficient: 6.2

Step 30.00062 = 6.2 × 10⁻⁴

Answer6.2 × 10⁻⁴

Example 3 SN → Standard

3.8 × 10⁵

Step 1Exponent 5 is positive.

Step 2Move decimal 5 places right.

Step 33.8 × 10⁵ = 380,000

Answer380,000

Common mistakes

What students write Counting zero digits instead of counting decimal places moved — for 0.0050, two leading zeros suggest 10⁻², but the decimal moves 3 places right to reach 5.0 × 10⁻³.

The fix Count the number of places the decimal MOVES until one non-zero digit sits before it. That move count, not the zero count, is |n|.

What students write Reading 4.7 × 10⁻³ as a negative number (−4,700) because the exponent is negative.

The fix A negative exponent means a SMALL positive number. 4.7 × 10⁻³ = 0.0047 — the negative tells which direction the decimal moves, not the sign of the result.

Teacher tip

Head off the two predictable errors before they happen. First: Count the number of places the decimal MOVES until one non-zero digit sits before it. That move count, not the zero count, is |n|. Second: A negative exponent means a SMALL positive number. 4.7 × 10⁻³ = 0.0047 — the negative tells which direction the decimal moves, not the sign of the result.