Reading, building, expanding and comparing whole numbers to one billion
Predict
Write 6 × 10⁷ + 4 × 10⁴ + 6 in standard form. Pause the video and write your answer.
Show me
60 040 006 — also written 60,040,006.
Quick check
Which power of ten equals one billion?Show me
10⁹ — one billion is 1 followed by nine zeros.
Write 205 030 008 in expanded form using powers of ten. Pause the video and write it down.Show me
2 × 10⁸ + 5 × 10⁶ + 3 × 10⁴ + 8 × 10⁰. A final + 8 is also correct.
Compare 620 405 000 and 620 450 000.Show me
620 405 000 < 620 450 000 — first difference in the ten-thousands place: 0 < 5.
Recap. Read a number one period at a time. Expand it with one term per non-zero digit. Build it back by placing digits and filling zeros down to the ones. Compare digit counts first, then digits from the left.
B1.2 Perfect squares and square roots
Perfect squares and square roots
Predict
Is each number a perfect square? If not, name the nearby perfect squares. Pause the video and decide.
Show me
90 is not; it lies between 81 and 100. 121 = 11² and 64 = 8² are perfect squares.
Quick check
9² = ?Show me
81 — nine times nine.
√144 = ?Show me
12 — because 12 × 12 = 144.
Is 50 a perfect square? Explain.Show me
No. Fifty lies between 49 and 64, so no whole number squared equals 50.
Recap. Squaring multiplies a number by itself. The radical symbol gives the non-negative square root. Perfect squares through 144 are useful benchmarks.
B1.3 Reading, comparing, and ordering rational numbers
Reading, comparing, and ordering rational numbers
Predict
Order the four values from least to greatest. Which pair is closest? Pause the video and write your order.
Show me
−2/5, −0.25, 3/10, 0.301. The closest pair is 3/10 = 0.300 and 0.301.
Quick check
Which is smaller: −0.8 or −0.25?Show me
−0.8 — it lies farther left.
Name one useful strategy for comparing fractions and decimals.Show me
Rewrite them in a common exact form, such as exact decimals or equivalent fractions.
Name one value between −3/4 and −1/2. Pause and decide.Show me
−5/8 is one example; −0.6 also works.
Recap. Rational numbers can be represented exactly in different forms. Farther right means greater. Choose a useful common exact form when comparison is difficult.
B1.4 Equivalent fractions and lowest terms
Equivalent fractions and lowest terms
Predict
Write each fraction in lowest terms. Pause the video and write your answers.
Show me
18/24 = 3/4. 7/15 is already in lowest terms. −10/25 = −2/5.
Quick check
What change guarantees an equivalent fraction?Show me
Multiply or divide numerator and denominator by the same non-zero factor.
24/36 in lowest terms?Show me
2/3 — divide both by 12.
When is a fraction in lowest terms?Show me
When no common factor greater than 1 remains.
Recap. Multiplicative scaling preserves a fraction's value. To simplify, find the greatest common factor and divide numerator and denominator by it.
B1.5 Generating rational numbers between two quantities
Finding rational numbers between two rational numbers
Predict
Give one value between each pair, and show your method. Pause the video and work it out.
Show me
17/24 lies between 2/3 and 3/4. 1.245 lies between 1.24 and 1.25. Other answers are possible.
Quick check
Name a decimal between 0.3 and 0.4.Show me
0.35 is one example.
3/5 and 4/5 have adjacent numerators. How can you find a fraction between them?Show me
Rewrite both with a finer denominator: 6/10 and 8/10, so 7/10 fits.
How many rational numbers lie between two distinct rational numbers?Show me
Infinitely many.
Recap. Put the endpoints in a comparable exact form. Choose a value strictly between them. If needed, partition the interval more finely. Averaging gives the exact midpoint.
B1.6 Rounding decimal numbers
Rounding decimal numbers
Predict
Round each number as asked, always from the original. Pause the video and write your answers.
Show me
4.2, 4, and −4.2.
Quick check
What should you find before using a rounding shortcut?Show me
The two neighbouring benchmarks.
3.456 to the nearest whole number?Show me
3.
Why avoid double rounding?Show me
The first rounding can change information needed for the second.
Recap. Find the neighbouring benchmarks and choose the closer one. At an exact midpoint, use the stated convention. Round negatives by distance, and always round from the original value.
B1.7 Fractions, decimals, and percents
Fractions, decimals, and percents
Predict
Complete both rows. Which rule did you use first? Pause the video and write your answers.
Show me
0.6 = 3/5 = 60%.3/8 = 0.375 = 37.5%.
Quick check
What does percent mean?Show me
Per hundred.
3/8 as a decimal?Show me
0.375 — three divided by eight.
1.25 as a percent?Show me
125% — multiply by 100.
Recap. Fraction to decimal: divide. Decimal to percent: multiply by 100. Percent to decimal: divide by 100. Percent to fraction: write per 100, clear decimals if needed, then simplify.