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Place Value, Decimals & Scientific Notation Lab

See every digit's role with a color-coded place value chart. Convert freely between decimals, fractions, and percentages. Express numbers in scientific notation and discover which fractions produce repeating decimals.

Guided Experiment: Powers of 10

What happens to each digit's place value when you multiply or divide a number by 10? How does the decimal point appear to move?

Write your hypothesis in the Lab Report panel, then click Next.

Place Value Chart

thousands
3
3,000
hundreds
4
400
tens
5
50
ones
6
6
.
tenths
7
0.7
hundredths
8
0.08
3 × 1,000 = 3,0004 × 100 = 4005 × 10 = 506 × 1 = 67 × 0.1 = 0.78 × 0.01 = 0.08

Controls

Place Value Analysis

Expanded Form
3000+400+50+6+0.7+0.083000 + 400 + 50 + 6 + 0.7 + 0.08
Word Form
three thousand four hundred fifty-six and seven eight hundredths
Digit Breakdown
thousands3 × 1,000 = 3,000
hundreds4 × 100 = 400
tens5 × 10 = 50
ones6 × 1 = 6
tenths7 × 0.1 = 0.7
hundredths8 × 0.01 = 0.08

Data Table

(0 rows)
#NumberExpanded FormScientific NotationFractionPercent
0 / 500
0 / 500
0 / 500

Reference Guide

Place Value System

Each digit's value depends on its position. Moving left multiplies by 10. Moving right divides by 10.

3,456.78=3,000+400+50+6+0.7+0.083{,}456.78 = 3{,}000 + 400 + 50 + 6 + 0.7 + 0.08

The expanded form shows the contribution of each digit to the total value.

Decimal, Fraction & Percent

Every number can be written as a decimal, fraction, or percent. They are three forms of the same value.

0.75=34=75%0.75 = \frac{3}{4} = 75\%

To convert a decimal to a percent, multiply by 100. To convert a fraction, divide numerator by denominator.

Scientific Notation

Scientific notation expresses numbers as a coefficient (between 1 and 10) multiplied by a power of 10.

602,200,000,000,000,000,000,000=6.022×1023602{,}200{,}000{,}000{,}000{,}000{,}000{,}000 = 6.022 \times 10^{23}

Large numbers get positive exponents. Small numbers (like 0.000001) get negative exponents.

Repeating vs Terminating Decimals

A fraction terminates as a decimal if and only if its denominator (in lowest terms) has only factors of 2 and 5.

18=0.125 (terminates),13=0.333… (repeats)\frac{1}{8} = 0.125 \text{ (terminates)}, \quad \frac{1}{3} = 0.333\ldots \text{ (repeats)}

Denominators like 3, 6, 7, 9, 11 produce repeating decimals because they have prime factors other than 2 and 5.