What is the value of a digit?

Understanding the value of a digit is fundamental in mathematics. The value of a digit depends on its position in a number, which is known as its place value.

Place Value

Place value is the value of where a digit is in the number. For example, in the number 345, the digit 5 is in the ‘ones’ place, the digit 4 is in the ‘tens’ place, and the digit 3 is in the ‘hundreds’ place. This means:

  • The 5 represents 5 ones (or simply 5).
  • The 4 represents 4 tens (or 40).
  • The 3 represents 3 hundreds (or 300).

Example: Breaking Down a Number

Consider the number 2,573. To find the value of each digit:

  • The digit 3 is in the ‘ones’ place, so it represents $3 times 1 = 3$
  • The digit 7 is in the ‘tens’ place, so it represents $7 times 10 = 70$
  • The digit 5 is in the ‘hundreds’ place, so it represents $5 times 100 = 500$
  • The digit 2 is in the ‘thousands’ place, so it represents $2 times 1000 = 2000$

Adding these values together, we get $2000 + 500 + 70 + 3 = 2573$

Powers of Ten

Each place in a number represents a power of ten. Starting from the right, the first place is $10^0$ (ones), the second place is $10^1$ (tens), the third place is $10^2$ (hundreds), and so on. This is why the digit’s place value increases by a factor of ten as you move to the left.

Example: Large Numbers

For a larger number like 47,682, the place values are:

  • The digit 2 is in the ‘ones’ place ($10^0$), so it represents $2 times 1 = 2$
  • The digit 8 is in the ‘tens’ place ($10^1$), so it represents $8 times 10 = 80$
  • The digit 6 is in the ‘hundreds’ place ($10^2$), so it represents $6 times 100 = 600$
  • The digit 7 is in the ‘thousands’ place ($10^3$), so it represents $7 times 1000 = 7000$
  • The digit 4 is in the ‘ten thousands’ place ($10^4$), so it represents $4 times 10000 = 40000$

Adding these values together, we get $40000 + 7000 + 600 + 80 + 2 = 47682$

Decimal Numbers

Place value also applies to decimal numbers. For example, in the number 3.142, the place values are:

  • The digit 3 is in the ‘ones’ place ($10^0$), so it represents $3 times 1 = 3$
  • The digit 1 is in the ‘tenths’ place ($10^{-1}$), so it represents $1 times 0.1 = 0.1$
  • The digit 4 is in the ‘hundredths’ place ($10^{-2}$), so it represents $4 times 0.01 = 0.04$
  • The digit 2 is in the ‘thousandths’ place ($10^{-3}$), so it represents $2 times 0.001 = 0.002$

Adding these values together, we get $3 + 0.1 + 0.04 + 0.002 = 3.142$

Conclusion

Understanding the value of a digit through place value is essential for grasping how numbers work. It helps us read, write, and interpret numbers correctly, whether they are whole numbers or decimals.

3. BBC Bitesize – Place Value

Citations

  1. 1. Khan Academy – Place Value
  2. 2. Math is Fun – Place Value

Related

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H + HO2 → O2 + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O2 k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) H + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-5 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M⁻¹ s⁻¹) 1 OH + H₂ → H + H₂O 3.74 x 10⁷ 2 OH + HO₂ → HO₂ + OH⁻ 5 x 10⁹ 3 OH + H₂O₂ → HO₂ + H₂O 3.8 x 10⁷ 4 OH + O₂ → O₂ + OH 9.96 x 10⁹ 5 OH + HO₂ → O₂ + H₂O 7.1 x 10⁹ 6 OH + OH → H₂O₂ 5.3 x 10⁹ 7 OH + e⁻aq → OH⁻ 3 x 10¹⁰ 8 H + O₂ → HO₂ 2.0 x 10¹⁰ 9 H + HO₂ → H₂O₂ 2.0 x 10¹⁰ 10 H + H₂O₂ → OH + H₂O 3.44 x 10⁷ 11 H + OH → H₂O 1.4 x 10¹⁰ 12 H + H → H₂ 1.94 x 10¹⁰ 13 e⁻aq + O₂ → O₂⁻ 1.9 x 10¹⁰ 14 e⁻aq + O₂ → HO₂⁻ + OH⁻ 1.3 x 10¹⁰ 15 e⁻aq + HO₂ 2.0 x 10¹⁰ 16 e⁻aq + H₂O₂ 1.1 x 10¹⁰ 17 e⁻aq + HO₂ → OH + OH⁻ 1.3 x 10¹⁰ 18 e⁻aq + H⁺ → H 2.3 x 10¹⁰ 19 e⁻aq + e⁻aq → H₂ + OH⁻ + OH⁻ 2.5 x 10⁹ 20 HO₂ + O₂ → O₂ + HO₂ 1.3 x 10⁹ 21 HO₂ + HO₂ → O₂ + H₂O₂ 8.3 x 10⁵ 22 HO₂ + HO₂ → O₂ + OH + H₂O 3.7 23 HO₂ + HO₂ → O₂ + O₂ + OH + H₂O 7 x 10⁵ s⁻¹ 24 H⁺ + O₂⁻ → HO₂ 4.5 x 10¹⁰ 25 H⁺ + O₂⁻ → O₂ 2.0 x 10¹⁰ 26 H⁺ + OH⁻ 1.4 x 10¹¹ 27 H⁺ + HO₂⁻ 2 x 10¹⁰ 28 H₂O₂ → HO₂ + H⁺ + OH⁻ 2.5 x 10⁻⁵ s⁻¹ 29 H₂O₂ → H⁺ + OH⁻ 1.4 x 10⁻⁷ s⁻¹ 30 O₂ + O₂ → O₂ + HO₂ + OH⁻ 0.3 31 O₂ + H₂O₂ → O₂ + OH + OH 16 32

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O + O → 2 OH k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ